Question

Thomas the giant gorilla stood on a bridge 624 feet above the water below. He picked up a car threw it off the bridge with an initial velocity of 50 feet per second. How long will it take the car to splash into the water below?

Answer 1

8

Step-by-step explanation:

Answer 2

The car will take approximately 4.865 seconds to splash into the water.

Step-by-step explanation:

Let suppose that car moves initially downwards. We must see the kinematics of the car after being thrown off the bridge, it is quite certain that car experiment a free fall, in which it is accelerated uniformly by gravity. The time spent by the car to splash into the water is obtained from this equation of motion:

`y = y_(o)+v_(o)\cdot t +(1)/(2)\cdot g \cdot t^(2)`

Where:

`y` - Current height, measured in feet.

`y_(o)` - Initial height, measured in feet.

`v_(o)` - Initial velocity, measured in feet per second.

`t` - Time, measured in seconds.

`g` - Gravitational acceleration, measured in feet per square second.

If we know that
`y = 0\,ft`,
`y_(o) = 624\,ft`,
`v_(o) = -50\,(ft)/(s)` and
`g = -32.174\,(ft)/(s^(2))`, this quadratic function is obtained:

`-16.087\cdot t^(2)-50\cdot t +624 = 0`

Now we get the roots of the polynomial by Quadratic Formula:

`t_(1) \approx 4.865\,s`,
`t_(2) \approx -7.973\,s`

Only the first root is physically reasonable. In a nutshell, the car will take approximately 4.865 seconds to splash into the water.