Suppose the ball is kicked horizontally with an initial speed of 9.37m/s. If the ball travels a horizontal distance of distnace 85 meters, how tall is the mountain?
R = 9.39T = 85m.
T = 9.05s = Time in flight.
Tr - Tf = T/2 = 9.05 / 2 = 4.53s. = Rise time = Fall time.
h = V0*t + 0.5g*t^2,
h = 0 + 4.9(4.53)^2 = 101m.
To find the height of the mountain, we need to consider the horizontal and vertical motion of the ball.
Let's first analyze the horizontal motion. The ball is kicked horizontally with an initial speed of 9.37 m/s, and it travels a horizontal distance of 85 meters. We can use the horizontal distance formula:
distance = speed * time
The distance traveled horizontally is 85 meters, and the speed is 9.37 m/s. Since there is no horizontal acceleration, the time taken to cover the horizontal distance is the same as the time the ball is in the air.
85 = 9.37 * time
Solving for time:
time = 85 / 9.37
Now, let's consider the vertical motion of the ball. The ball undergoes free-fall motion vertically, and the vertical distance can be calculated using the formula:
distance = (1/2) * acceleration * time^2
Since the ball is kicked horizontally, there is no initial vertical velocity (vy = 0). The only force acting on the ball in the vertical direction is gravity, resulting in an acceleration of approximately 9.8 m/s^2 (ignoring air resistance).
Plugging in the known values:
distance = (1/2) * 9.8 * (85 / 9.37)^2
Now calculate:
distance = (1/2) * 9.8 * (85 / 9.37)^2
The calculated value of distance will give us the vertical distance covered by the ball. This distance represents the height of the mountain.