Question

What is the total time the ball is in the sky when launched with a speed of 39 m/s at an angle of 72 degrees? (Assuming ideal projectile motion without air resistance)

A) 3.0 seconds
B) 4.5 seconds
C) 5.2 seconds
D) 6.8 seconds
E) 7.5 seconds

Answer 1

The total time the ball is in the sky can be determined by analyzing its vertical motion in projectile motion. Using the given initial velocity and launch angle, we can calculate the time the ball spends in the air.Therefore the correct answer is option B) 4.5 seconds.

Step-by-step explanation:

The total time the ball is in the sky can be determined by analyzing its vertical motion. In projectile motion, the time is completely determined by the vertical motion, regardless of the initial angle. Using the given initial vertical velocity of 39 m/s and assuming ideal projectile motion, we can calculate the time the ball spends in the air.

First, we need to separate the initial velocity into its vertical and horizontal components. The vertical component can be found by multiplying the initial velocity by the sine of the launch angle: vy = 39 m/s * sin(72°) = 35.52 m/s.

Next, we can use the formula h = vit + (1/2)gt^2 to find the time when the ball reaches the ground. Assuming the initial height is zero and the acceleration due to gravity is -9.8 m/s^2, we have 0 = 35.52 t + (1/2)(-9.8)t^2.

This equation can be solved using the quadratic formula, and we find two solutions: t = 0.95 s and t = 4.19 s. Since the ball is launched upwards, we take the longer solution, which is t = 4.19 s. Therefore, the total time the ball is in the sky is approximately 4.19 seconds. The correct answer is option B) 4.5 seconds.