An object is projected with a velocity of 100 ms-1 from the ground level at an angle 0 to the vertical. If the total time of flight of the projectile is 10 ...

An object is projected with a velocity of 100 ms^-1 from the ground level at an angle 0 to the vertical. If the total time of flight of the projectile is 10 s, calculate θ. (g = 10 ms^-2).

Answer Details

When an object is projected at an angle to the vertical, it moves in a curved path called a projectile motion. The horizontal and vertical motions of the projectile are independent of each other. The time of flight is the total time taken by the projectile to reach the maximum height and return to the ground level. Let's denote θ as the angle of projection. We can use the following equations to solve for θ: Time of flight = 2usinθ/g where u is the initial velocity and g is the acceleration due to gravity. In this case, u = 100 ms^-1 and the time of flight = 10 s. Therefore, 10 = 2 x 100 x sinθ / 10 Simplifying, we get sinθ = 0.5 To find θ, we take the inverse sine (sin^-1) of 0.5, which gives us θ = 30°. Therefore, the answer is θ = 30°.