How Does a Flare Fired from a Moving Truck Behave?

[lilmixbrunette1]

Problem:
A flare was fired straight up at a speed of 25 m/s from the bed of a truck traveling along a level road at a speed of 15 m/s.

a. Assuming the flare landed back in the bed of the truck, how much time was the flare in the air?

b. How far horizontally did the flare travel before landing back in the bed of the truck?

c. What maximum height did the flare reach?



Some equations that i thought might help with this problem are
deltaX=vi+deltaT*1/2adeltaT^2
but since i do not no the cange in X or the time i can not use this equation



To try and figure out this problem i made a chart showing what horizontal and vertical things that i already knew

H V
0=ax ay=10 m/s^2
15 m/s=Vxi Vyi=25 m/s
=deltaX deltaXy=
deltaT=​

thank you for your time

 

[denverdoc]

One other eqn, Y=Yo+vo(t)+1/2g*t^2 where both Y and Yo are the same in this case, landing in the bed. Remember vo (initial y velocity and acceleration are opposite, just solve for t. The horizontal dispacement is easily computed knowing time and that ax=0. See if you can figure out the third part.

PS: most of the gravity problems are symmetrical, so time to top is just
vf=v0+at where vf=0, and the total trip up and down twice that.

 

[m2003]

and effort in solving this problem. First, let's define a few variables to make things clearer:

- v0 = initial velocity of the flare (25 m/s)
- v0x = initial horizontal velocity of the flare (15 m/s)
- v0y = initial vertical velocity of the flare (25 m/s)
- a = acceleration due to gravity (10 m/s^2)
- t = time in flight

a. To calculate the time the flare was in the air, we can use the equation v = v0 + at, where v is the final velocity (in this case, 0 m/s since the flare landed back in the truck). Rearranging the equation, we get t = (v - v0)/a. Plugging in the values, we get t = (0 - 25)/(-10) = 2.5 seconds. Therefore, the flare was in the air for 2.5 seconds.

b. To calculate the horizontal distance the flare traveled, we can use the equation d = v0xt, where d is the distance traveled. Plugging in the values, we get d = (15)(2.5) = 37.5 meters. Therefore, the flare traveled 37.5 meters horizontally before landing back in the truck.

c. To calculate the maximum height the flare reached, we can use the equation vf^2 = v0^2 + 2ad, where vf is the final vertical velocity (in this case, 0 m/s since the flare reached its maximum height) and d is the maximum height. Rearranging the equation, we get d = (vf^2 - v0^2)/(2a). Plugging in the values, we get d = (0^2 - 25^2)/(2(-10)) = 31.25 meters. Therefore, the maximum height the flare reached was 31.25 meters.

I hope this helps in solving the problem. Keep in mind that these equations assume no air resistance and a constant acceleration due to gravity. Real-life situations may vary.