A body is thrown with initial velocity 50ms-1 at the angle 60• With the horizontal. Calculate the horizontal range ,also calculate what another angle achieve the same?

To calculate the horizontal range of a projectile, we need to consider the initial velocity and the launch angle.

1. Horizontal Range Calculation:
The horizontal range is the distance traveled by the projectile in the horizontal direction before hitting the ground. It can be calculated using the formula:

Range = (Initial Velocity^2 * sin(2*Launch Angle)) / g

where:
Initial Velocity = 50 m/s (given)
Launch Angle = 60 degrees (given)
g = acceleration due to gravity = 9.8 m/s^2

Now let's substitute these values into the formula and calculate the horizontal range:

Range = (50^2 * sin(2*60)) / 9.8
Range = (2500 * sin(120)) / 9.8
Range = (2500 * (√3/2)) / 9.8
Range = (2500 * √3) / (2 * 9.8)
Range ≈ 374.24 meters

Therefore, the horizontal range of the projectile is approximately 374.24 meters.

2. Finding the Angle for the Same Range:
To find another angle that would result in the same horizontal range, we need to solve the equation which relates the range to the launch angle. The equation can be rearranged as follows:

Range = (Initial Velocity^2 * sin(2*Launch Angle)) / g

Since we know the initial velocity, the current launch angle, and the range, we can solve for the new launch angle:

sin(2*New Launch Angle) = (Range * g) / Initial Velocity^2
2*New Launch Angle = arcsin((Range * g) / Initial Velocity^2)
New Launch Angle = (1/2) * arcsin((Range * g) / Initial Velocity^2)

Let's substitute the known values and calculate the new launch angle:

New Launch Angle = (1/2) * arcsin((374.24 * 9.8) / 2500)
New Launch Angle ≈ 14.8 degrees

Therefore, another angle of approximately 14.8 degrees will achieve the same horizontal range of 374.24 meters.