A waterfall has a hit of 1500 ft. A pebble is thrown upward at the velocity of 24ft per second. The hot, h, of the pebble after t seconds is given by the equation h=-16t+24t+1500. How long after the pebble is thrown will it hit the ground.

A waterfall has a height of 1500 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet per second. The height, h, of the pebble after t seconds is given by the equation h =−16t^2+24t+1500. How long after the pebble is thrown will it hit the ground?

Pebble will hit the ground after 10.46 seconds.

Step-by-step explanation:

Given:

The height, "h" of the pebble after t seconds, "h" = −16t^2+24t+1500

We have to find the time it will take to hit the ground.

For this we have to put h = 0 and solve the quadratic.

Quadratic formula:

⇒ Standard equation :

⇒

Now,

Solving the above equation with quadratic formula after comparing its values with the standard equation.

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⇒

⇒

⇒

⇒

⇒                         ⇒

⇒                                ⇒

⇒                            ⇒

Discarding the negative values.

The pebble will hit the ground after 10.46 seconds.