Answer:
Step-by-step explanation:
The motion of the projectile can be modeled using the following kinematic equation:
h = vi*t + (1/2)at^2
where h is the height of the projectile, vi is the initial velocity, a is the acceleration due to gravity (approximately -9.8 m/s^2), and t is the time elapsed.
We want to find the time it takes for the projectile to reach a height of 375 m, so we can set h = 375 and solve for t:
375 = 100t + (1/2)(-9.8)*t^2
Simplifying and rearranging, we get:
4.9t^2 + 100t - 375 = 0
We can solve this quadratic equation using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / (2*a)
where a = 4.9, b = 100, and c = -375.
Plugging in the values, we get:
t = (-100 ± sqrt(100^2 - 44.9(-375))) / (2*4.9)
Simplifying, we get:
t = (-100 ± sqrt(10000 + 7350)) / 9.8
t = (-100 ± sqrt(17350)) / 9.8
We take the positive value of t, since we are only interested in the time it takes for the projectile to reach a height of 375 m:
t = (-100 + sqrt(17350)) / 9.8
t ≈ 21.43 seconds (rounded to two decimal places)
Therefore, it takes the projectile approximately 21.43 seconds to reach a height of 375 m.