A waterfall has a height of 1300 feet.

Question

A waterfall has a height of 1300 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The height,h, of the pebble after t seconds is given by the equation h=-16t+16t+1300. How long after the pebble is thrown will it hit the ground?

Answer 1

James, this implies h=0 when the pebble hits the ground.

 

0=-16t^2+16t+1300 would be the correct equation.

 

You could factor out 4 from the equation to simplify the equation

 

4(-4t^2+4t+325)=-4t^2+4t+325=0

 

Use the quadratic formula.

 

t=(-4±√(4^2-4(-4)(325)))/(2*(-4))=(-4±√(16+16*325)))/-8

t=(-4±4√(1+325))/-8=(-4±4√326)/-8

 

t≅9.52s  or t≠-8.52s

 

Therefore, it would take about 9.52 seconds for the pebble to hit the ground.