I have a few basic physics problems.
How do you calculate how long it will take for an object to hit the ground when it is dropped from a certain height? Specifically from 128 ft.
Additionally how would you calculate how much velocity is needed to launch at item to a certain height? Specifically from 64 ft.
Thanks :)
What do you think first
Well, for the first I was trying to use V(t)=g(t)+v(0), but I can't figure out of v(t) would be zero because it hit the ground or if I need to figure it out some other way.
The second one I think is probably the same as figuring out what velocity it is when you drop it from 64ft. That's as far as I got.
To calculate how long it will take for an object to hit the ground when dropped from a certain height, you can use a simple equation based on the laws of motion. In this case, you can use the equations of motion for free fall. The equation you need is:
h = (1/2) * g * t^2
Where:
- h is the height from which the object is dropped
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
To calculate the time it takes for the object to hit the ground, you need to rearrange the equation to solve for t:
t = sqrt(2h / g)
Now, let's plug in the values for your specific scenario. Since you provided the height in feet, we need to convert it to meters first:
h = 128 ft * 0.3048 m/ft ≈ 39.0144 m
Plugging in the values, we get:
t = sqrt(2 * 39.0144 m / 9.8 m/s^2) ≈ 2.03 seconds
So, it will take approximately 2.03 seconds for the object to hit the ground when dropped from a height of 128 ft.
Now let's move on to calculating the velocity needed to launch an object to a certain height. The equation we can use in this case is based on the conservation of energy:
v^2 = u^2 + 2gh
Where:
- v is the final velocity at the desired height
- u is the initial velocity (which is usually 0 for objects dropped)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the desired height
Rearranging the equation to solve for the final velocity, we get:
v = sqrt(2g * h)
Again, let's convert the desired height from feet to meters:
h = 64 ft * 0.3048 m/ft ≈ 19.5072 m
Plugging in the values, we have:
v = sqrt(2 * 9.8 m/s^2 * 19.5072 m) ≈ 19.9071 m/s
So, you would need a velocity of approximately 19.9071 m/s to launch an object to a height of 64 ft.