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Chapter 7 Projectile Motion

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The motion of an object that has been thrust into air where the only forces acting on it are gravity & air resistance.

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Projectile Motion Because we ignore air resistance, the only force acting on thrown objects is gravity.

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Projectile The object that has been given an initial thrust, fired, or thrown into air.

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Trajectory The path of a projectile as it travels through space.

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In Projectile Motion The vertical & horizontal components act independently & can be solved independently

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In Projectile Motion The only force acting vertically is the force of gravity causing downward acceleration.

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In Projectile Motion There are no net forces acting horizontally; thus, the horizontal velocity is constant.

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In Projectile Motion Use your velocity formulas to solve for vertical & horizontal motion independently.

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In Projectile Motion Solve for time in air 1 st Always use the vertical component to solve for the time in air.

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In Projectile Motion After solving for the time in air, solve for the range or horizontal distanced traveled

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A rock has been thrown horizontally at 4.0 m/s from a tower 49 m high. Calculate: t air, d H, and v H & v V the instant before impact:

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A bullet exits a 0.50 m barrel horizontally at 1000.0 m/s from a height of 2.0 m. Calculate: a bullet in barrel, t in barrel, t air,v V at impact, d H :

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A plane flying horizontally at 250 m/s at an altitude of 4.9 km high drops a bomb. Calculate: t air, d H, and v V the instant before impact:

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A ball rolls at 75 cm/s off the edge of a 49 cm table. Calculate: t air, d H, and v V the instant before impact:

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A car traveling at 1500 cm/s goes off the edge of a 0.49 km high cliff. Calculate: t air, d H, and maximum v V :

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A car accelerates at 5.0 m/s 2 for 250 m before going off the edge of a 0.49 km high cliff. Calculate: t & max v on the ground, & t, d H, and max v V in air:

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A cannon ball is fired at 1000.0 m/s at 53 o from horizontally. Calculate: max height, t air,v V at impact, d H :

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Repeat the last problem with a cannon ball exiting the barrel at the same speed with angles of 40 o, 45 o, & 50 o

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Assumming all factors are the same for that cannon, Calculate its maximum range:

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A ball is thrown at 25 m/s at 45 o from horizontal. Calculate: t air, maximum height, v V at impact, d H :

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A 25 Mg car is accelerated from rest at 5.0 m/s 2 up a 250 m ramp at 37 o from horizontal. Calculate: t, & v f on the ramp, and d V, d H, t, and maximum v V in air:

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A 1.0 Mg block slides from rest down a 250 m ramp ( = 0.20) at 37 o from horizontal that ends 490 m above the ground. Calculate: t, & v f on the ramp, and d H, t, and maximum v V in air:

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Review

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A sled coasts off a 0.49 km cliff at 18 km /hr. Calculate: t air, max v V, & d H :

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A catapult launches a 250 kg rock at 100.0 m/s at 37 o from horizontal. Calculate: t up, d V, t air, & d H :

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Define each of the following DistanceDisplacement SpeedForce Velocity Acceleration

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Give Units for each of the following DistanceDisplacement Speed Acceleration VelocityForce

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v f = v i + at d = v i t + ½ at 2 v f 2 = v i 2 + 2ad

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Projectile Motion Projectile Trajectory

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A 25 Mg sled slides from rest down a 500.0 m slope ( = 0.10) at 37 o from horizontal that ends 2.45 km above the ground. Calculate: t, & v f on the slope, and d H, t air, and the maximum v V in air:

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A 250 Mg sled accelerates at 3.0 m/s 2 up a 250 m ramp ( = 0.25) at 53 o from horizontal. Calculate: F a, t ramp, v f ramp, t air, d v, & d H

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A 0.10 Mg cycle is accelerated with a force of 500.0 N for 10.0 s before hitting a 25 m ramp at 37 o from horizontal. Draw the system and Calculate: v at bottom & top of ramp, and t, d v, & d H in the air

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An airplane is flying horizontally due west at 360 km/hr at an altitude of 0.49 km & drops a 2000 lb bomb. Draw the system and Calculate: t air, maximum v V, & d H.

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A 50.0 kg person skis ( = 0.010) down a 3.0 km ski trail with an average slope of 30 o. Draw the system and Calculate: a, t, maximum v on the trail

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British Ships had cannons with muzzle velocities of 400 m/s while the cannons at Ft McHenry could fire at 500 m/s. The British could elevate to 45 o while the Americans could elevate to 18 o. Which cannons had the greater range.

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Expanding gases produce about 10,000 N of force in a gun barrel. One nation wants to build a cannon that will deliver a 2,000 kg cannon ball 200 km. Calculate the length that the barrel must be. Because you are estimating round g to –10 m/s 2.

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A B = 37 o = 53 o Y = 1.00 kN X Y C

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A B C F H of A F H of B WYWY W x + F V of C F H of C F V of AF V of B + F V of C

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A B C F H of B WYWY W x + F V of C F H of C F V of A F V of B F V of C F H of A

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A 200.0 kg rock is catapulted at 53 o from horizontal at about 0.10 km/s. Draw the system and Calculate: t, d v, & d H in the air

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A rock is thrown at 37 o from horizontal at about 25 m/s. Draw the system and Calculate: t, d v, & d H in the air

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