On a distant planet, golf is just as popular as it is on earth. A golfer tees off and drives the ball 4.9 times as far as he would have on earth, given the same velocities on both planets. The ball is launched at a speed of 54 m/s at an angle of 42° above the horizontal. When the ball lands, it is at the same level as the tee.

Question

On a distant planet, golf is just as popular as it is on earth. A golfer tees off and drives the ball 4.9 times as far as he would have on earth, given the same velocities on both planets. The ball is launched at a speed of 54 m/s at an angle of 42° above the horizontal. When the ball lands, it is at the same level as the tee.

(a) On the distant planet, what is the maximum height of the ball?
1 m

(b) On the distant planet, what is the range of the ball?
2 m

Answer 1

To find the maximum height of the ball and the range on the distant planet, we can use the equations of projectile motion. Here's how you can calculate them step by step:

Step 1: Separate the motion into horizontal and vertical components.
The initial velocity of the ball has a horizontal component (Vx) and a vertical component (Vy).
Vx = V * cos(θ), where V is the speed of the ball (54 m/s) and θ is the launch angle (42°).
Vy = V * sin(θ)

Step 2: Calculate the time of flight (t) for the ball.
The time of flight can be determined from the vertical component of velocity using the equation:
t = 2 * Vy / g, where g is the acceleration due to gravity (on Earth, approximately 9.8 m/s²).

Step 3: Calculate the maximum height (H) reached by the ball.
The maximum height can be found using the equation:
H = (Vy^2) / (2 * g)

Step 4: Calculate the range (R) of the ball.
The range, or horizontal distance traveled by the ball, can be calculated using the equation:
R = Vx * t

Now, let's plug in the values and calculate the answers:

(a) Maximum height (H) on the distant planet:
Vx = 54 m/s * cos(42°) ≈ 38.754 m/s
Vy = 54 m/s * sin(42°) ≈ 36.184 m/s
t = 2 * Vy / g ≈ 7.397 s
H = (Vy^2) / (2 * g) ≈ 66.557 m

Therefore, the maximum height of the ball on the distant planet is approximately 66.557 meters.

(b) Range (R) on the distant planet:
R = Vx * t ≈ 38.754 m/s * 7.397 s ≈ 286.324 m

Therefore, the range of the ball on the distant planet is approximately 286.324 meters.

Please note that the exact answer may depend on the specific values of acceleration due to gravity and other factors on the distant planet.