SOLUTION: A bullet is fired from a gun and made a projectile motion. The trace of the path of the bullet is mathematically expressed as d = 60t — 4t2, where d is the distance in meters of

Question 1165760: A bullet is fired from a gun and made a projectile motion. The trace of the path of the bullet is mathematically expressed as d = 60t — 4t2, where d is the distance in meters of the bullet from the ground in t seconds.
a. What is the distance of the bullet from the ground after 2 seconds (s)?
b. At what time will the bullet reach a height of 200 m?
c. What maximum distance from the ground does the bullet reach?
d. After how many seconds does the bullet reach its highest point?
e. At what time will the bullet hit the ground?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
d=60t-4t^2
so d(2)=120-16=104 m.
200=-4t^2+60t
so 4t^2-60t=200=0
and
t^2-15t+50=0, dividing by 4
(t-10)(t-5)=0
so at t = 5 and 10 seconds

maximum distance up is at the vertex or t=-b/2a That is 60/8 or 7.5 seconds.
d(7.5)=450-225=225 m
It hits the ground after 15 seconds, twice the time it takes to reach the highest point.
one could also do 4t^2-60t=0
t^2-15t=0
t(t-15)=0
t=0 (start) and t=15 seconds.

RELATED QUESTIONS
A bullet fired from a gun travels a distance of 4750 ft in 3.2 seconds. Find the average... (answered by jim_thompson5910)

A.) A bullet is fired from a gun perfectly horizontal towards the center of a target 200... (answered by jorel1380)

What is the velocity of a bullet? if a gun is fired straight upward, the bullet leave... (answered by stanbon)

Velocity of a bullet. A gun is fired straight upward. The bullet leaves the gun at 100... (answered by ankor@dixie-net.com)

A certain .22 caliber gun fires a bullet at a speed of 1192 feet per second. If the .22... (answered by ankor@dixie-net.com)

a gun is fired straight upward. the bullet leaves the gun at 100 feet per second (time... (answered by stanbon)

I am having a problem trying to solve this linear equation word problem. Velocity of a (answered by scott8148)

When a bullet is fired from a loosely held rifle,the ratio of the mass of the bullet to... (answered by ikleyn)

6. Speeding Bullet Problem: The speed of a bullet is traveling depends on the number of... (answered by vleith)