Question

34. Height of a Projectile If a rocket is fired vertically into the air with a speed of 240 feet per second, its height at timet seconds is given by h(t) = -16+ 240t. At what time(s) will the rocket be the following number of feet above the ground? a. 704 feet b. 896 feet c. Why do parts a and b each have two answers? d. How long will the rocket be in the air? (Hint: How high is it when it hits the ground?) e. When the equation for part d is solved, one of the answers is t = 0 second. What does this represent?

Answer 1

(a) when the height is 704 feet, so -16t²+240t = 704 , => -16t²+240t -704=0, => t=4seconds, t=11seconds. Answer

(b) when the height is 894 feet, so -16t²+240t = 894, => -16t²+240t-894 =0, => t=7 seconds & t=8seconds. Answer

(c) because rocket path is a parabolic path and at the above-mentioned height in option a and b, the rocket was at two times , one at the time of ascending and other at the time of descending.

(d) make h(t) =0 , so -16t(t-15)=0 , hence t=15 Seconds , Answer

(e) it represents that at t=0, body was at height =0,means at starting point height =0