Projectile Facts and Sample Problems  

Marshmallow Projectile Project

 Problem: An object is projected upward with a velocity of 100. m/s.
a) to what height will it rise?
b) how long will it take it to reach that height?
c) what will be the total elapsed time until it strikes the earth?
d) how fast will it be going when it strikes the earth?

Solution: a) Find height of projectile by using:

             h = v²/2 g    à    (100 m/s)² / 2 * 9.8 m/s²  =  10 000 m²/s²  /  19.6 m/s²   =  510. m

 b)    The time required to reach the apex (highest altitude) is the same amount of time as the fall time (time to fall from a certain height for all objects)

1) to find time knowing distance use:

                t = Ö2d/g      à   Ö2 * 510. m / 9.8 m/s²  =  Ö104 s²  =  10.2 s

2)    double fall time to find total time in flight (or cut total time in flight in half to find fall time or time to reach apex) total flight time = 10.2 s + 10.2 s = 20.4 s

 c)    The velocity at the apex will be 0 m/s for the instant the projectile is neither going up or coming.down.

 d)    The acceleration of gravity is always acting on the body, although it may weaken very slightly with increased altitude.

 e)    The final velocity, height, and fall time of projectiles are independent of mass. We will neglect air resistance or other outside forces.

f)    To find final velocity:

          V_f  =  Ö2 g d    à  Ö2 * 9.8 m/s² * 510. m  =  99.99 m/s  or 100. m/s

 g)    Starting velocity (take-off velocity) must be equal to final velocity. This assumes total parachute failure.

 h)    Potential and kinetic energies must be conserved due to the Law of Conservation of Energy (will all due respects to entropy).

 Sample Problems: '

 1.    A baseball player hits a fly ball to a height of 44 m (about 144 feet). After the bat strikes the ball, how much time will there be for a fielder to get into position to make the catch?

 2.    A projectile is fired into the air and 18 seconds later hits the ground (with total parachute failure)
a) how high did it travel?
b) how fast was it going when it hit the ground?
c) how long did it take to reach its maximum altitude?
d) with what speed was the projectile fired into the air
e) calculate the total kilometers the projectile traveled?

3.    A projectile is launched at a speed of 357.6 m/s. The parachute fails and the projectile falls (free fall) back to earth.
a) how many seconds does it take the projectile to reach its apex?
b) how high does the projectile travel?
c) how fast is the object traveling just before it strikes the earth?
d) what is the total time the projectile is in flight?
e) how far up does the projectile travel in 20 seconds?