Question

A projectile is launched vertically from the ground into the air with initial velocity v0. It reaches the ground in 10 minutes. Assume that the height of the projectile above the ground after t minutes is given by h(t) = −5t 2 + v0t. Find the initial velocity v0 of the projectile.

Answer 1

The initial velocity of the projectile is 50 meters per minute

Step-by-step explanation:

The equation that describes the height (h on meters) of the projectile as a function of time (t in minutes) is:

`h(t)=\left(-5(m)/(min^(2))\right)\,t^(2)+v_(0)\,t`(1)

We already know at 10 minutes the projectile reaches the ground, so if we assume our coordinate system on the ground that implies h(10 min)=0m, using this on (1):

`0=\left(-5(m)/(min^(2))\right)\,(10\,min)^(2)+v_(0)\,(10\,min)`

solving for
`v_(0)`:

`v_(0)=(\left(5(m)/(min^(2))\right)\,(10\,min)^(2))/((10\,min))=50\,(m)/(min)`

Note: It’s important to have a careful use of units in this kind of problem to avoid errors in the units of our answers, if we are calculating velocity we should get velocity units.