A body is thrown with some velocity at an angle of 60° with the horizontal. If its horizontal component is 50ms-1, what is the actual velocity
Question
A body is thrown with some velocity at an angle of 60° with the horizontal. If its horizontal component is 50ms-1, what is the actual velocity
Solution
The problem involves a body thrown at an angle, which means we are dealing with a case of projectile motion. In such a case, the initial velocity of the body is split into two components: a horizontal component (Vx) and a vertical component (Vy).
Given in the problem is the horizontal component of the velocity (Vx), which is 50 m/s. We are asked to find the actual (initial) velocity of the body.
The horizontal and vertical components of the velocity can be related to the initial velocity (V) and the angle of projection (θ) using the following equations:
Vx = V * cos(θ) Vy = V * sin(θ)
We can rearrange the equation for Vx to solve for V:
V = Vx / cos(θ)
Substituting the given values:
V = 50 m/s / cos(60°)
Note that cos(60°) = 0.5
So,
V = 50 m/s / 0.5 = 100 m/s
Therefore, the actual (initial) velocity of the body is 100 m/s.
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