To solve this problem:
1. Determine the horizontal and vertical components of the initial velocity:
vx = 150 ft/s * cos(52°)
vx = 150 ft/s * 0.6157
vx = 92.355 ft/s
vy = 150 ft/s * sin(52°)
vy = 150 ft/s * 0.7880
vy = 118.2 ft/s
2. Solve for the time it takes for the ball to hit the ground:
Use the kinematic equation: y = yo + vot + 0.5at^2
Where:
y = 4.8 ft (final height)
yo = 0 ft (initial height)
vo = 118.2 ft/s (initial vertical velocity)
a = -32 ft/s^2 (acceleration due to gravity)
4.8 = 0 + (118.2)t + 0.5(-32)t^2
4.8 = 118.2t - 16t^2
16t^2 - 118.2t + 4.8 = 0
Solving this quadratic equation gives t = 5.77 seconds
Therefore, the correct answer is:
*5.77 seconds
a baseball player hits a ball at an angle of 52* and at a height of 4.8 ft. if the ball's initial velocity after being hit is 150 ft./s and if no one catches the ball, when will it hit the ground? remember that the acceleration due to gravity is 32 ft./s^2
*5.77 seconds
*5.82 seconds
*7.43 seconds
*7.39 seconds
1 answer