Answer to Question #138902 in Physics for Tom

Question

A student kicks a soccer ball with an initial velocity of 12.0 m/s at a fence at an angle θ = 53 degrees, which is a height 3.5 meters and is a distance of 5.0 meters away from where they kicked the ball. The ball hits nothing in flight while in flight and air resistance is negligible.

sin 53 degrees = 0.80
cos 53 degrees = 0.60
tan 53 degrees = 1.33

A. Determine the initial horizontal and vertical velocity vox and voy of the ball.

B. Determine the time it takes for the ball to reach the fence.

C. Will the ball hit the fence? If so, how far below the top of the fence will it hit? If not, how far above the top of the fence will it pass?

D. The student repeats the kick in a flat field with no fence, it lands at the same vertical position it was kicked from.

i. How much time does the ball spend in the air?
ii. Determine the horizontal distance the ball will travel.

Answer 1

a)

$$V_{0x}=12(0.6)=7.2\frac{m}{s}\\V_{0y}=12(0.8)=9.6\frac{m}{s}$$

b)

$$t=\frac{5}{7.2}=0.69\ s$$

c) No.

$$y=9.6(0.69)-0.5(9.8)(0.69)^2=4.3\ m$$

$$y-h=4.3-3.5=0.8\ m$$

d) i)

a)

$$t=\frac{2(12)(0.8)}{9.8}=2.0\ s$$

ii)

$$R=\frac{(12)^2(2(0.8)(0.6))}{9.8}=14\ m$$