Problema Solution
Marco is throwing a tennis ball at a kite that is stuck 42 feet up in a tree, trying to know it loose. He can throw the ball at a velocity of 45 feet per second upward at a height of 4 feet. Will his throw reach the kite? How hard does Marco need to throw the ball to reach the kite?
Answer provided by our tutors
The formula for height, in feet, of a projectile under the influence of gravity is given by:
h = -16t^2 + vt + s,
where t is the time in seconds, v is the upward initial velocity (at t = 0), and s is the starting height.
In our case we have:
v = 45 ft/s
s = 4 ft
h = -16t^2 + 45t + 4
The ball will reach the height if h max >= 45 ft.
h max = c - b^2/4a, where a = -16, b = 45, c = 4
h max = 4 - 45^2/(4*(-16))
h max = 35.64 ft
Since 36.54 ft < 46 ft follows the throw will never reach the kite.