A projectile is launched from ground level with an initial velocity of v_(0) feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=-16t^2+v_(0)t Find the time(s) that the projectile will (a)reach a heig of 288 ft and (b) return to the ground when v_(0)=144 feet per second. (a) Find the time(s)that the projectile will reach a height of 288 ft when v_(0)=144 feet per second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. square seconds (Use a comma to separate answers as needed.) B. The projectile does not reach 288 feet.

Question

Answer 1

To find the time(s) that the projectile will reach a height of 288 feet, we need to solve the equation

for

when

and

.Substituting the given values into the equation, we have:

Rearranging the equation, we get:

Dividing both sides of the equation by -16, we have:

Now, we can solve this quadratic equation using factoring or the quadratic formula. Let's try factoring first:

Setting each factor equal to zero, we have:

or

Solving for

, we get:

or

Therefore, the correct answer is:A. 3 seconds, 6 seconds

Soru