Question

Boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal. how long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and 8 = 9.80 m / 52?

Answer 1

The rock takes 1.57 seconds to reach the maximum height of its trajectory.

Step-by-step explanation:

To find the time it takes for the rock to reach the maximum height of its trajectory, we can use the equation for vertical motion:

Final Velocity (Vf) = Initial Velocity (Vi) + Acceleration (a) * Time (t)

At the maximum height, the final velocity will be zero because the rock is momentarily at rest before falling back down. The initial velocity in the vertical direction is determined by the initial velocity and the launch angle:

Vi_y = Vi * sin(θ)

Using the formula, we can find the time it takes to reach the maximum height:

t = Vi_y / g

Substituting the given values:

t = 3.13 m/s * sin(30°) / (9.80 m/s^2)

t = 1.57 s