For a science fair competition, a group of High School students built a kicker-m

Question

For a science fair competition, a group of High School students built a kicker-machine that can launch a golf ball from the origin with a velocity of 12.9 m/s and initial angle of 31.3° with respect to the horizontal.
(a) Where will the golf ball fall back to the ground?
(b) How high will it be at the highest point of its trajectory?
(c) What is the ball's velocity vector (in Cartesian components) at the highest point of its trajectory? First enter x, then y.
(d) What is the ball's acceleration vector (in Cartesian components) at the highest point of its trajectory? First enter x, then y

Explanation / Answer

First, take the initial velocity and angle and convert to x, y coordinates
x = cos 31.3* 12.9m/s = 11.02m/s
y = sin 31.3* 12.9m/s = 6.7m/s

Then find the time to the top
t = v-vy/g = 0-6.7/-9.8 = 0.68s

Now find the total distance x = vx *t = 11.02*(0.68*2) = 14.99m
To find height, y = vy*t + 1/2gt2 = 6.7 *0.68 + 1/2 *-9.8 * 0.682 = 2.27m

At the highest point, velocity = (11.02, 0)m/s since there is no vertical velocity at the top

At the highest point, acceleration = (0, -9.8)m/s2 since acceleration is only in vertical direction

Hope that helps

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