Freshman Physics Major here

It should come down at the exact same speed. Considering we are taking out the affect of air and wind.

>>7698892
https://en.wikipedia.org/wiki/Equations_of_motion#Constant_translational_acceleration_in_a_straight_line

Remember that throughout its flight, as long as you negate air friction, potential energy + kinetic energy are always the same.

Example:
PE1 + KE1 = PE2 + KE2

Here is projectile equation. Can also be used for most velocity equations.
d = (1/2)gt^2 + vt

d is distance (in this case height)
g is gravity (on earth 9.81 m/s^2)
v is starting velocity
t is time

Also, please convert everything to meter, meters/second, ect.

Dont use imperial system unless you like to get assfucked

>>7698963
g can be switch with a for acceleration

>>7698892
You can't say how high you are throwing a ball and how fast,

With a speed of 10 mph and no acceleration I think your ball is only going up 1 meter or something like that

>>7698913
This is your solution in this case
Just take you acceleration as -9.81 m/s and take the integral of that for your speed and the integral of that for your displacement with v(0) being 4.47 m/s and y(0) being 0

>>7698999
This just occurred to me, maybe OP meant he's 50 ft up in the air and he throws it with initial velocity of 10 mph and he wants to know it's speed when it hits the ground.

>>7699007
In that case you need to change y(0) from 0 to 50 ft converted into meters

>>7699007
No I meant, if a ball goes 10mph from the ground to a 50ft mark, will it travel down at 10mph too or will it speed up as it travels back down?

>>7699059
Your ball wil not go 50 feet in the air, more like 3 feet

>>7698892
So your pic related is orthogonality of Legendere polynomials, but what you actually want help on is motion?

>>7699084
you're assuming gravitational attraction is the only force acting on the ball, but OP didn't mention that. he explicitly stated the ball goes 50 ft up.

>>7698892
In high school physics air resistance is left away, because it's too difficult to calculate.
Is there, however, a way to calculate it? If we know the size of the ball and it's speed

>>7701742
the force due to drag is proportional to the velocity of the object [math] F_{ \gamma }= \gamma v [/math] where gamma is the drag coefficient. You'll come across this in differential equations and it's actually only part of the picture. As you said shape plays a part too. This kind of motion is known as damped motion and the coefficient depends on the thickness of the fluid. A system can be underdamped, overdamped, or critically damped. I think this only applies to harmonic motion and not drag in general.