Question

A golf ball was struck from the first tee at Lunar Golf and Country Club. It was given a velocity of 48 m/s at an angle of 40˚ to the horizontal. On the moon, gravity = -1.6 m/s2.

A) What are the vertical and horizontal components of the ball's initial velocity?
B)For what interval of time is the ball in flight?
C)How far will the ball travel horizontally?

Answer 1

The vertical and horizontal components of the ball's initial velocity are 30.71 m/s and 36.76 m/s, respectively. The ball is in flight for 38.14 seconds. The ball will travel horizontally for 1404.69 meters.

Step-by-step explanation:

To find the vertical and horizontal components of the ball's initial velocity, we can use trigonometry. The vertical component is given by the formula Vv = V * sin(θ), where V is the magnitude of the velocity (48 m/s) and θ is the angle (40°). So, Vv = 48 * sin(40°) = 30.71 m/s. The horizontal component is given by the formula Vh = V * cos(θ), so Vh = 48 * cos(40°) = 36.76 m/s.

To find the time of flight, we can use the formula T = 2 * Vv / g, where g is the acceleration due to gravity (-1.6 m/s^2). Plugging in the values, we get T = 2 * 30.71 / -1.6 = 38.14 seconds.

The horizontal distance traveled by the ball can be found using the formula D = Vh * T. Plugging in the values, we get D = 36.76 * 38.14 = 1404.69 meters.