Jimmy shot a basketball from a height of four feet with an upward velocity of 12 feet/sec.
1. Write an equation to model this situation.
2. Will Jimmy’s ball make it to the ten-foot tall hoop?
Jimmy shot the basketball from a height of four feet with an upward velocity of 12 ft/sec. The acceleration due to gravity is 32 ft/sec^2.
Take the independent variable as the time elapsed after the ball is thrown and the dependent variable as the height of the ball.
y = f(t) = 4 + 12*t - (1/2)*32*t^2 = 4 + 12*t - 16t^2
The height of the basketball plotted against time is a parabola. The highest point of the parabola is the value of y at t which is the solution of f'(t) = 0.
f'(t) = 12 - 32t
12 - 32t = 0
=> t = 12/32
At t = 32/12, y = 4 + 12*(12/32) - 16*(12/32)^2
=> 4 + 4.5 - 2.25
The maximum height of the ball is 6.25 ft. It does not make it to the ten-foot tall hoop.