Example Problems Projectile Motion

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

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

Initial Velocity of the ball V=d/t 108/3.12 V=34.6

Find the x component of the velocity just before it hits the ground The same as the initial velocity

Find the y component of the velocity just before it hits the ground V=gt V=-9.8*3.12 V=-30.5765 m/s ***Remember it is falling down and gravity would be negative

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?

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

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

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.

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?

At what speed does the vehicle move along its descent path? 31.6 m/s R 53.6 m/s a2+b2=c2

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)

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?

A is asking for the vertical distance D=1/2gt2

B is asking for horizontal distance D=vt