A projectile is projected from the origin with a velocity of 45.0 m/s at an angle of 30.0 degrees above the horizontal. What is the time it takes for the projectile to hit the ground?
A) 2.54 s
B) 3.02 s
C) 4.59 s
D) 5.31 s
E) 6.04 s

Question

Quizplus · Accepted Answer

We can use the kinematic equations to solve for the time it takes for the projectile to hit the ground. We know that the initial vertical velocity is 45.0 sin(30.0) = 22.5 m/s, and the acceleration due to gravity is -9.81 m/s^2. We want to find the time when the projectile hits the ground, so we set the vertical position to be 0. We can use the equation:
y = yo + vot + (1/2)at^2
where y = 0, yo = 0, vo = 22.5 m/s, a = -9.81 m/s^2, and we solve for t:
0 = 0 + 22.5t - (1/2)(9.81)t^2
0 = 45t - 4.905t^2
Solving for t using the quadratic formula, we get t = 4.59 s (ignoring the negative root, since time cannot be negative). Therefore, the answer is C.

A Projectile Is Projected from the Origin with a Velocity