(a) -32t+10 = 0
(b) see (a) above
(c) use (a) in p(t)
(d) solve p(t)=0
(e) use (d) in v=-32t+10
Suppose we are standing on top of a 300-ft tower and we are holding a shiny new penny.We do not hurt it down, for that would be dangerous and wrong! We toss it up at a velocity of 10 feet per second and then when it comes down it just happens to plummet to the ground below
At a time t seconds after the toss, the velocity is given by v(t)=-32t+10.Its distance from the sidewalk, in feet, is given by p(t)=-16t^2+1-t+300
a. At what time is the penny's velocity zero?
b. When is the penny at its highest point?
c. What is the maximum height achieved by the penny?
d. How long is te penny in the air?
e.How fast is it going when it hits the ground?
2 answers
The penny's height at any time, t, seconds would be given by the equation h(t)=-16t²+10t+300. It reaches its' maximum height at -10/-32, or 0.3125 seconds (-b/2a). This gives it a maximum height of 301.5625 ft. The penny lands at h(t)=0, or 16t²-10t-300=0; so total time in the air would be 4.6539 seconds. Its' velocity would be -32(4.6539)+10, or -138.9248 ft/sec downward