Posted by **chica** on Thursday, May 13, 2010 at 6:40pm.

A diver on a platform 40 feet in height jumps upward with an initial velocity of 5 feet per sec. His height in h feet after t seconds is given by the function h=-16t^2+5t+50. What is his maximum height? How long will it take him to reach the surface of the water?

- Algebra-Quadratic Applications -
**Reiny**, Thursday, May 13, 2010 at 7:02pm
There is a discrepancy in your problem.

You state the platform is 40 feet high, yet the equation suggests an initial height of 50 feet.

You would find the vertex of the downwards parabola.

An easy way is to find the x of the vertex by -b/2a

= -5/(-32) = 5/32 seconds

Now sub that back in to find the height when t = 5/32

for the last part,

set -16t^2 + 5t + 50 = 0

and solve for t using the quadratic formula.

- Algebra-Quadratic Applications -
**Damon**, Thursday, May 13, 2010 at 7:10pm
I assume you have not covered calculus which would make this easy.

Without calculus you must complete the square to find the vertex of the parabola.

h=-16t^2+5t+50

-h = 16 t^2 - 5t - 50

50 - h = 16 t^2 - 5 t

50/16 -h/16 = t^2 -(5/16) t

50/16 - h/16 + 25/1024 = t^2 -5/16 t + 25/1024

3225/1024 - h/16 = (t-5/32)^2

we are at the top when t = 5/32

and h = 3225/64 = 50.4

Now what is t when h = 0?

= -16 t^2 +5 t + 50

t = [ -5 +/- sqrt (25 + 3200) ]/-32

t = [-5 + 56.8 ]/-32 = -1.62

ignore that solution, negative time was before we started

t = [-5 - 56.8]/-32 = 1.93 seconds

## Answer This Question

## Related Questions

- math - A diver on a platform 40 feet in height jumps upward with an initial ...
- Algebra II - If an object is propelled upward from a height of 16 ft at an ...
- Math - Please help ! 1.)a catapult launches a boulder with an upward velocity of...
- calculus - the height in feet of a rocket from ground level is given by the ...
- Algebra 1 - Key: *** = my answer 8. A catapult launches a boulder with an upward...
- Math - A model airplane is shot up from a platform 1 foot above the ground with ...
- algebra - The height in feet of a projectile with an initial velocity of 32 feet...
- Algebra - A high diver is standing on a platform above a pool. Her diving path ...
- math - A ball is thrown into the air with an upward velocity of 20 ft/s. Its ...
- Word problem - . A catapult launches a boulder with an upwark velocity pf 184 ...

More Related Questions