What was the initial velocity of the ball when it was kicked at an angle of 37° to a goalkeeper who is 24m away?
The initial velocity of the ball when it was projected is 15.64 m/s.
Calculation of the Initial Velocity:
The initial velocity of the ball is calculated using the formula for the range of projectile which is given by:
R = (u^2 sin(2θ)) / g
Where:
- R is the range of the projectile (given as 24m)
- u is the initial velocity of the ball
- θ is the angle of projection (given as 37°)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
By rearranging the formula for initial velocity, we get:
u = √((Rg) / sin(2θ))
Substituting the given values into the formula:
u = √((24 * 9.8) / sin(2 * 37))
u = √(235.2 / sin(74))
u = √(235.2 / 0.96)
u = √244.5
u ≈ 15.64 m/s
Therefore, the initial velocity of the ball when it was projected at an angle of 37° to a goalkeeper who is 24m away is 15.64 m/s.