A man can throw a stone 50m away.what is the maximum height to which he can throw the same stone?

To calculate the maximum height to which a stone can be thrown, we can use the concept of projectile motion. The key assumption here is that there is no air resistance.

The vertical motion of the stone follows a parabolic path, where the highest point along the trajectory is the maximum height.

In this case, we are given the horizontal distance, which is 50m. So, we need to find the corresponding maximum height.

To solve for the maximum height, we need to use the formula for the range of the projectile:

Range = (initial velocity^2 * sin(2*angle)) / gravity

Since we're interested in the maximum height, we can determine the initial velocity using the given range and the angle.

The formula for range can be rewritten as:

Range = (v^2 * sin(2*angle)) / gravity

We can rearrange this formula to solve for the initial velocity:

v = sqrt((Range * gravity) / sin(2*angle))

Substituting the given values:
Range = 50m
angle = 45 degrees (assuming the optimal angle for maximum range)
gravity = 9.8 m/s^2 (acceleration due to gravity)

Plugging in these values, we can calculate the initial velocity:

v = sqrt((50 * 9.8) / sin(90)) ≈ 31.3 m/s

Now, we can calculate the maximum height using the formula for vertical motion:

Maximum height = (initial velocity^2 * sin^2(angle)) / (2 * gravity)

Using the calculated initial velocity and angle of 45 degrees:

Maximum height ≈ (31.3^2 * sin^2(45)) / (2 * 9.8) ≈ 39.8 meters

Therefore, the maximum height to which the man can throw the stone is approximately 39.8 meters.

depends on how long it takes to travel the 50 meters.

Given a sufficient speed, it could reach any desired height.