Chapter 7 Projectile Motion

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

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

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

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

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

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

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

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

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

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

A rock has been thrown horizontally at 4. 0 m/s from a tower 49 m high A rock has been thrown horizontally at 4.0 m/s from a tower 49 m high. Calculate: tair, dH, and vH & vV the instant before impact:

A plane flying horizontally at 250 m/s at an altitude of 4 A plane flying horizontally at 250 m/s at an altitude of 4.9 km high drops a bomb. Calculate: tair, dH, and vV the instant before impact:

Drill: A ball rolls at 75 cm/s off the edge of a 49 cm table Drill: A ball rolls at 75 cm/s off the edge of a 49 cm table. Calculate: tair, maximum vV, and dH:

A car traveling at 1500 cm/s goes off the edge of a 0.49 km high cliff. Calculate: tair, dH, and maximum vV:

A car accelerates at 5.0 m/s2 for 250 m before going off the edge of a 0.49 km high cliff. Calculate: t & max v on the ground, & t, dH, and max vV in air:

Drill: A bullet exits a 0. 50 m barrel horizontally at 500 Drill: A bullet exits a 0.50 m barrel horizontally at 500.0 m/s from a height of 2.0 m. Calculate: (a & t)in barrel, (t, max vV, & dH)in air:

A cannon ball is fired at 1000. 0 m/s at 53o from horizontal A cannon ball is fired at 1000.0 m/s at 53o from horizontal. Calculate: max height, tair ,vV at impact, dH:

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

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

Drill: A ball is thrown at 25 m/s at 45o from horizontal. Calculate: tair, hmax, vV max, dH:

A ball is thrown at 25 m/s at 53o from horizontal A ball is thrown at 25 m/s at 53o from horizontal. Calculate: vV, vH, tair, hmax, & dH

A 25 Mg car is accelerated from rest at 5 A 25 Mg car is accelerated from rest at 5.0 m/s2 up a 250 m ramp at 37o from horizontal. Calculate: t, & vf on the ramp, and dV, dH, t, and maximum vV in air:

A 1. 0 Mg block slides from rest down a 250 m ramp (m = 0 A 1.0 Mg block slides from rest down a 250 m ramp (m = 0.20) at 37o from horizontal that ends 490 m above the ground. Calculate: t, & vf on the ramp, and dH, t, and maximum vV in air:

Review

A sled coasts off a 0.49 km cliff at 18 km /hr. Calculate: tair, max vV, & dH:

A catapult launches a 250 kg rock at 100. 0 m/s at 37o from horizontal A catapult launches a 250 kg rock at 100.0 m/s at 37o from horizontal. Calculate: tup, dV, tair, & dH :

Define each of the following Distance Displacement Speed Force Velocity Acceleration

Give Units for each of the following Distance Displacement Speed Acceleration Velocity Force

vf = vi + at d = vit + ½ at2 vf2 = vi2+ 2ad

Projectile Motion Projectile Trajectory

A 25 Mg sled slides from rest down a 500. 0 m slope (m = 0 A 25 Mg sled slides from rest down a 500.0 m slope (m = 0.10) at 37o from horizontal that ends 2.45 km above the ground. Calculate: t, & vf on the slope, and dH, tair, and the maximum vV in air:

A 250 Mg sled accelerates at 3. 0 m/s2 up a 250 m ramp (m = 0 A 250 Mg sled accelerates at 3.0 m/s2 up a 250 m ramp (m = 0.25) at 53o from horizontal. Calculate: Fa, tramp, vf ramp, tair, dv, & dH

A 0. 10 Mg cycle is accelerated with a force of 500. 0 N for 10 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 37o from horizontal. Draw the system and Calculate: v at bottom & top of ramp, and t, dv, & dH in the air

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: tair, maximum vV, & dH.

A 50. 0 kg person skis (m = 0. 010) down a 3 A 50.0 kg person skis (m = 0.010) down a 3.0 km ski trail with an average slope of 30o. Draw the system and Calculate: a, t, maximum v on the trail

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 45o while the Americans could elevate to 18o. Which cannons had the greater range.

Expanding gases produce about 10,000 N of force in a gun barrel 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/s2.

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

A B C Wx + WY FV of C a b FV of A FV of B + FV of C FH of A FH of C FH of B C FH of C Wx + FV of C WY

A B C Wx + WY FV of C a b FV of A FV of B FH of A FH of C FH of B

A 200. 0 kg rock is catapulted at 53o from horizontal at about 0 A 200.0 kg rock is catapulted at 53o from horizontal at about 0.10 km/s. Draw the system and Calculate: t, dv, & dH in the air

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