To find the time taken by the object to reach the highest point, we can analyze the vertical motion of the projectile. The initial velocity can be resolved into its vertical and horizontal components:
Vertical component (Vy): Vy = V * sin(θ) Horizontal component (Vx): Vx = V * cos(θ)
Given: Initial velocity (V) = 100 m/s Launch angle (θ) = 60° Acceleration due to gravity (G) = 10 m/s² (assuming it's directed downwards)
Using the equation for vertical displacement in uniformly accelerated motion:
Δy = Vy * t - (1/2) * G * t²
At the highest point, the vertical displacement (Δy) is zero, and the final vertical velocity (Vy) is zero. Therefore, we can set up the equation:
0 = Vy * t - (1/2) * G * t²
Substituting the values: 0 = (100 m/s * sin(60°)) * t - (1/2) * 10 m/s² * t²
Simplifying the equation:
0 = (50 * √3) * t - 5t²
Rearranging the terms:
5t² = (50 * √3) * t
Dividing both sides by t:
5t = 50 * √3
Simplifying further:
t = (50 * √3) / 5 t = 10 * √3
So, the time taken by the object to reach the highest point is approximately 10 * √3 seconds.