A boy can throw a ball a maximum horizontal distance of R on a level field. How far can he throw the same ball vertically upward? Assume that his muscles give the ball the same speed in each case. (Use R and g as appropriate in your equation.)
R/2
The time to travel the distance R is t = R/V.
With the same velocity being imparted to the ball upward, the vertical distance traveled becomes
h = V(R/V) - g(R/V)^2/2
= R - (g/2)(R/V)^2
R/5
r/2
To solve this problem, we can use the concept of projectile motion. When an object is thrown vertically upwards, it follows a parabolic trajectory and reaches some maximum height before falling back down.
The time taken for the ball to reach its maximum height can be determined using the equation:
t = vertical speed / acceleration due to gravity (g)
Since the initial vertical speed is the same as the initial horizontal speed, we can write:
t = initial speed / g
The distance traveled vertically can be calculated using the equation for displacement in vertical motion:
vertical distance = (initial speed)^2 / (2 * g)
Since the initial speed is the same in both horizontal and vertical directions, we can substitute it with R:
vertical distance = R^2 / (2 * g)
Therefore, the boy can throw the ball vertically upward to a distance of R^2 / (2 * g).