a body is projected at an angle of 60degree to the horizontal with a velocity of 150m/s calculate the time it take to reach the greatest height
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To calculate the time it takes for a body to reach its greatest height, you need to consider the vertical motion of the projectile. Here's how you can solve it step by step:
1. Separate the initial velocity into its vertical and horizontal components. The vertical component (Vv) can be calculated using the formula: Vv = V * sin(θ), where V is the initial velocity of the projectile and θ is the launch angle.
Given that the initial velocity (V) is 150 m/s and the launch angle (θ) is 60 degrees:
Vv = 150 m/s * sin(60°) = 150 m/s * √(3)/2 ≈ 129.9 m/s
2. Use the formula for vertical motion to find the time it takes for the body to reach its maximum height. The formula is: t = Vv / g, where g is the acceleration due to gravity (9.8 m/s²).
t = 129.9 m/s / 9.8 m/s² ≈ 13.26 seconds (rounded to two decimal places)
Therefore, it takes approximately 13.26 seconds for the body to reach its greatest height when projected at an angle of 60 degrees with a velocity of 150 m/s.