Question

A soccer player kicks a ball at an angle of 37∘from the horizontal with an initial speed of 50ft/sec. (A right triangle, one of whose angles is 37∘ , has sides in the ratio 3:4:5, or 6:8:10.) Assuming that the ball moves in a vertical plane. Find the time t₁ at which the ball reaches the highest point of its trajectory.

Answer 1

The time at which the ball reaches the highest point of its trajectory is 0.9375 seconds.

Step-by-step explanation:

To find the time at which the ball reaches the highest point of its trajectory, we need to take into account the initial speed and the angle at which it is kicked.

Since the ball moves in a vertical plane, we can break down its initial velocity into horizontal and vertical components:

Horizontal component: Vx = V * cos(θ) = 50 ft/sec * cos(37°) = 40 ft/sec

Vertical component: Vy = V * sin(θ) = 50 ft/sec * sin(37°) = 30 ft/sec

The time it takes for the ball to reach its highest point can be found using the formula: t1 = Vy / g, where g is the acceleration due to gravity (32 ft/sec2).

Substituting the values, we get: t1 = 30 ft/sec / 32 ft/sec2 = 0.9375 sec.