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Example Problems Projectile Motion

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**A ball is thrown horizontally from the top of a building 47. 7 m high**

A ball is thrown horizontally from the top of a building 47.7 m high. The ball strikes the ground at a point 108 m from the base of the building. A. Find the time the ball is in motion. B. Find the initial velocity C. Find the x component of the velocity just before it hits the ground D. Find the y component of the velocity just before it hits the ground

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**The time the ball is in the air**

Is gravity effecting it? Yes, use the vertical equations. D=1/2gt2 √2d/g 2*47.7/9.8 √9.7=3.12s

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**Initial Velocity of the ball**

V=d/t 108/3.12 V=34.6

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**Find the x component of the velocity just before it hits the ground**

The same as the initial velocity

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**Find the y component of the velocity just before it hits the ground**

V=gt V=-9.8*3.12 V= m/s ***Remember it is falling down and gravity would be negative

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**An arrow is shot at a 33⁰ angle with the horizontal**

An arrow is shot at a 33⁰ angle with the horizontal. It has a velocity of 54 m/s A. How high will it go? B. What horizontal distance will it travel?

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**54m/s Sin 33 =y/54 Cos 33=x/54 Sin 33 *54 Cos 33 * 54= 45.28m/s**

33⁰ vy Vx Sin 33 =y/54 Sin 33 *54 =29.41 m/s Cos 33=x/54 Cos 33 * 54= 45.28m/s Vertical speed Horizontal speed

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**Look at your vertical equations**

D=1/2gt2 V=gt Let’s combine these two equations using substitution method. t=v/g d=1/2 g(v/g)2 d=44.13 m

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**Now lets solve for the horizontal distance.**

We solved for the horizontal velocity and now we need to find an equation for the horizontal distance. D=vt and because of the trajectory we need to use twice the time from the previous problem.

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**At what speed does the vehicle move along its descent path?**

A descent vehicle landing on the moon has a vertical velocity vector toward the surface of the moon of 31.6 m/s. At the same time, it has a horizontal velocity of 53.2 m/s. At what speed does the vehicle move along its descent path? At what angle with the vertical is its path?

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**At what speed does the vehicle move along its descent path?**

31.6 m/s R 53.6 m/s a2+b2=c2

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**At what angle with the vertical is its path?**

31.6 m/s R θ=? 53.6 m/s tan θ=o/a Θ=tan-1 (o/a)

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**Janet jumps off a high diving platform with a horizontal velocity of 2**

Janet jumps off a high diving platform with a horizontal velocity of 2.83 m/s and lands in the water 2.2s later. A. How high is the platform? B. How far from the base of the platform does she land?

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**A is asking for the vertical distance**

D=1/2gt2

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**B is asking for horizontal distance**

D=vt

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