A ball is kicked into the air with a speed of 10m per second at angle of 60 degrees to the horizontal (take g=10).
a) Calculate the horizontal and vertical speed of the ball
b) Calculate the ball's time of flight
c) Calculate the distance from the kicked point that the ball hits the ground.
Vx = v cosθ
Vy = v sinθ
h(t) = Vy*t - 5t^2
ball stops when h=0
ball has traveled Vx * t along the ground.
a) To calculate the horizontal and vertical speeds of the ball, we can use the given initial speed and angle.
The horizontal speed (Vx) remains constant throughout the motion and is given by the equation:
Vx = velocity * cos(angle)
Substituting the given values:
Vx = 10 m/s * cos(60 degrees)
Vx = 10 m/s * (0.5)
Vx = 5 m/s
So, the horizontal speed of the ball is 5 m/s.
The vertical speed (Vy) changes due to the effect of gravity. At the highest point of the motion, the vertical speed is zero. At all other points, the vertical speed can be determined using the equation:
Vy = velocity * sin(angle)
Substituting the given values:
Vy = 10 m/s * sin(60 degrees)
Vy = 10 m/s * (√3/2)
Vy = 10√3 / 2 m/s
Vy = 5√3 m/s
So, the vertical speed of the ball is 5√3 m/s.
b) The time of flight is the total time the ball remains in the air. We can calculate it using the equation:
Time of flight = (2 * vertical speed) / g
Substituting the given values:
Time of flight = (2 * 5√3 m/s) / 10 m/s^2
Time of flight = (√3) seconds
So, the time of flight for the ball is √3 seconds.
c) To calculate the distance from the kicked point that the ball hits the ground, we can use the horizontal speed and time of flight.
Distance = horizontal speed * time of flight
Substituting the given values:
Distance = 5 m/s * √3 seconds
Distance = 5√3 m
So, the distance from the kicked point that the ball hits the ground is 5√3 meters.