the shape of sugarloaf mt. in rio de janeiro, brazil is such that if you were to kick a soccer ball hard enough, it could land near the base of the mountain without hitting the mountain's side. Suppose the ball is kicked horizontally with an initial speed of 9.37 m/s. if the ball travels horizontal distance of 85.0 m, how tall is the mountain?
404m
The ball is in the air
T = (85 m)/9.37 m/s) = 9.1 s
Calculate how far it falls in that time. That will be the mountain height,
H = (g/2) T^2
This agrees with the formula given by JOHNNY
You will be ignoring air resistance, which is NOT a good assumption for a soccer ball travelling that far and fast. It will probably nearly reach a terminal velocity and quit accelerating
jdx
To solve this problem, we can use the principles of projectile motion. When a ball is kicked with an initial horizontal speed, it will follow a parabolic trajectory due to the influence of gravity.
Given:
Initial horizontal speed (Vx) = 9.37 m/s
Horizontal distance traveled (X) = 85.0 m
We need to find the height of the mountain (H).
The horizontal and vertical motion of the ball are independent of each other. So, let's first calculate the time taken by the ball to travel 85.0 m horizontally.
The horizontal distance (X) covered by an object can be calculated using the formula: X = Vx * t, where t represents the time taken.
Therefore, rearranging the equation, we have: t = X / Vx
Substituting the given values, we get: t = 85.0 m / 9.37 m/s ≈ 9.06 s (rounded to two decimal places)
Now, using the known value of time (t), we can determine the vertical distance (H) covered by the ball using the formula for vertical motion under constant acceleration:
H = 0.5 * g * t^2
where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Substituting the values, we have:
H = 0.5 * 9.8 m/s^2 * (9.06 s)^2
H ≈ 0.5 * 9.8 m/s^2 * 82.27 s^2
H ≈ 0.5 * 806.146 m
H ≈ 403.073 m
Therefore, the approximate height of the Sugarloaf Mountain in Rio de Janeiro is 403.073 meters.