AN OBJECT IS PROJECTED AT AN ANGLE OF 50° TO THE VERTICAL AND ATTAINS A MAXIMUM HEIGHT OF 60m in 20s. DETERMINE THE RANGE ATTAINED BY THE OBJECT(g=10m/s^-2).
To determine the range attained by the object, we need to find the horizontal distance it travels.
First, let's analyze the given information:
1. Angle of projection: 50° to the vertical.
2. Maximum height: 60m.
3. Time of flight: 20s.
4. Acceleration due to gravity: 10m/s^2.
Now, let's break down the motion of the object into vertical and horizontal components.
Vertical motion:
The maximum height reached by the object occurs when its vertical velocity becomes zero. At maximum height, the vertical velocity can be calculated using the equation:
vf = vi + gt
Since the object reaches maximum height, vf = 0, and using g = 10m/s^2:
0 = vi + 10 * t
Solving for the initial vertical velocity (vi):
vi = -gt
Substituting the known values, with g = 10m/s^2 and t = 20s:
vi = -10 * 20
vi = -200m/s
Horizontal motion:
The horizontal distance traveled by the object (range) can be determined using the equation:
Range = horizontal velocity * time of flight
To find the horizontal velocity, we need to find the initial horizontal velocity (vix) and final horizontal velocity (vfx). Since there is no horizontal acceleration, vix = vfx.
The initial horizontal velocity (vix) can be calculated using the initial vertical velocity (vi) and the angle of projection:
vix = vi * cos(angle)
Substituting the known values, with vi = -200m/s and the angle = 50°:
vix = -200 * cos(50°)
The final horizontal velocity (vfx) can be determined using the final vertical velocity (vf) and the angle of projection:
vfx = vf * cos(angle)
At maximum height, the final vertical velocity is zero, so vf = 0. Substituting the angle = 50°:
vfx = 0 * cos(50°)
vfx = 0
Since vix = vfx, we can consider the horizontal velocity (vx) to be vix.
Substituting the known values, we get:
vx = -200 * cos(50°)
Now, we can find the range by multiplying the horizontal velocity (vx) by the time of flight:
Range = vx * time of flight
Substituting the known values, with vx = -200 * cos(50°) and the time of flight = 20s:
Range = (-200 * cos(50°)) * 20
Using a calculator, we can evaluate the expression to get the range attained by the object.