If something is dropped at 89.478 mph from a height of 80 inches, how long will it take to hit the ground?

Question

jmartinez638 · Answer

How long will it take for the object to hit the ground, in seconds, and how far will it travel?

matt101 · Answer

If it's dropped from a height of 80 inches, that's how far it will travel. As for the time, you'll know that acceleration is equal to the change in speed over time. You know the initial speed (89.478 mph), the final speed is implied (0 mph, when the object hits the ground), and the acceleration (due to gravity). Use this information to calculate time!

jmartinez638 · Answer

but wouldn't the object go farther than the height of 80 inches because of its initial velocity? Or would it only travel 80 inches being dropped in those conditions?

jmartinez638 · Answer

@matt101

anonymous · Answer

$$\huge y_f=y_0+v_{0y}t+\frac{ 1 }{ 2 }g t^2$$You know the final y-position (0 because it hits the ground), and you know the initial height, initial velocity, and the gravitational acceleration constant (-9.8 m/s^2). I haven't gone through the math, but in case you need it:

`QUADRATIC FORMULA:`
$$\huge t=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }$$
If it is done correctly, you will get a negative value and a positive value. You can't have a negative time, so your answer will be the positive value.

jmartinez638 · Answer

I got about .945 seconds for the time it takes to hit the ground