To solve this problem, we need to first calculate the vertical component of the initial velocity of the ball. This can be done by using the formula:
Vy = V * sin(20°)
Vy = 110 ft/sec * sin(20°)
Vy = 110 ft/sec * 0.3420
Vy = 37.62 ft/sec
Next, we can calculate the time it takes for the ball to hit the ground using the formula:
h = Vy * t - 16t²
4.5 = 37.62 * t - 16t²
16t² - 37.62t + 4.5 = 0
Now, we can solve for t using the quadratic formula:
t = (-(-37.62) ± sqrt((-37.62)² - 4*16*4.5)) / (2*16)
t = (37.62 ± sqrt(1415.4244 - 288)) / 32
t = (37.62 ± sqrt(1127.4244)) / 32
t = (37.62 ± 33.60229) / 32
t = (37.62 + 33.60229) / 32 or t = (37.62 - 33.60229) / 32
t = 2.47 seconds or t = 0.0556 seconds
Since it's not possible for the ball to hit the ground in 0.0556 seconds, the time it takes for the ball to hit the ground is approximately 2.47 seconds.
Therefore, the answer is 2.47 seconds.
Question
A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20° above the ground from a height of 4.5 ft. Approximately how long does it take for the ball to hit the ground? Acceleration due to gravity is 32 feet per second squared.
(1 point)
Responses
2.35 seconds
2.35 seconds
2.47 seconds
2.47 seconds
6.46 seconds
6.46 seconds
6.50 seconds
1 answer