Math Question

Question

A projectile is launched from ground level with an initial velocity of v 0v feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s equals negative 16 t squared plus v 0 ts=−16t2+v0t. Find the time(s) that the projectile will (a) reach a height of 192 ft and (b) return to the ground when v 0v=128128 feet per second.
(a) Find the time(s) that the projectile will reach a height of 192 ft when v 0v=128128 feet per second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Answer 1

The equation for height is given as 

 

S= -16t² +V ₀ t

Also given 

 

V₀ = 128 ft/s

 

Substituting   192 = -16t² +128t

Which is simplified as 

t² -8t +12 =0

Which gives t = -2 sec and  t= 6 sec ( -2 can be ignored)

 

Using S = -16 *6*6 +128 *6 = 192 ft