Question

4. A golf ball resting on the ground is struck by a golf club and given an initial velocity of

50 m/s at an angle of 30° above the horizontal. The ball heads toward a fence 12 m high at
the end of the golf course, which is 200 m away from the point at which the golf ball was
struck. Neglect any air resistance that may be acting on the golf ball.
K
50 m/s
30⁰ go
200 m
Tout
a. Calculate the time it takes for the ball to reach the plane of the fence.
b. Will the ball hit the fence or pass over it?

Answer 1

To calculate the time it takes for the ball to reach the plane of the fence, we need to break down the initial velocity into its horizontal and vertical components. The time it takes for the ball to reach the fence can be found using the equation t = d / Vx, where d is the horizontal distance to the fence. Since the vertical distance fallen by the ball is greater than the height of the fence, the ball will hit the fence.

Step-by-step explanation:

To calculate the time it takes for the ball to reach the plane of the fence, we need to break down the initial velocity into its horizontal and vertical components. The horizontal component is given by Vx = V * cos(theta), where V is the initial velocity and theta is the angle of 30°. Substituting the given values, we get Vx = 50 m/s * cos(30°) = 43.3 m/s.

The time it takes for the ball to reach the fence can be found using the equation t = d / Vx, where d is the horizontal distance to the fence. Substituting the given values, we get t = 200 m / 43.3 m/s = 4.62 s.

Since the time it takes for the ball to reach the fence is 4.62 seconds, and the height of the fence is 12 m, we can calculate the vertical distance the ball falls during that time using the equation y = 1/2 * g * t^2, where g is the acceleration due to gravity. Substituting the values, we get y = 1/2 * 9.8 m/s^2 * (4.62 s)^2 = 104.5 m.

Since the vertical distance fallen by the ball is greater than the height of the fence, the ball will hit the fence.

Answer 2

See below

Step-by-step explanation:

Horizontal component of the velocity will carry the ball to the fence in how long?

Hor vel = 50 cos 30 = 43.3 m/s 200m / 43.3 m/s = 4.61 seconds

Vertical position given by

Df = vo t + 1/2 a t^2 with t = 4.61 secs vo = 50 sin 30

Df = height = 11 m <===== will not clear the fence