Question

A ball is kicked upward with an initial velocity of 52 feet per second. The ball's height, h (in feet), from the ground is modeled by 4072-03-02-07-00_files/i0130000.jpg, where t is measured in seconds. How much time does the ball take to reach its highest point? What is its height at this point?
a.
1.625 sec; 84.5 ft

c.
3.25 sec; 42.25 ft

b.
1.625 sec; 42.25 ft

d.
3.25 sec; 126.75 ft

Answer 1

The maximum vertical distance should be calculated through the equation,
                                d = (Vf² - Vi²) / 2a
Where Vf is the final veloity, Vi is the initial velocity and a is the acceleration due to gravity (32.1740 ft/s²). Substituting the known values,
                               d = (0 - 52²) / 2(-32.1740 ft/s²) 
                                     d = 42.02 ft
The time it will take for ball to travel this distance is calculated through the equation,
                                   d = (Vo)(t) - 0.5gt²
Substituting the known values.
                                    d = (52)(t) - 0.5*32.1740t²
The value of time is 1.60 s. Thus, the nearest answer to this item is answer B.