# Mechanics velocity of a bullet questions

Hello, i have a few questions i am doing and am wondering if someone would be kind enough to check i am doing them correctly

First question is..

A shot is fired horizontally at a target 20m away and it is notice3d that the bullet hits a point 7.5cm below the target aimed at. What was the velocity of the bullet when it left the pistol?

I get vertically
u=0ms^1 a=9.8ms^2 s=0.075m need t
so i used s=ut+0.5at^2
=0.075m=4.9t^2
t^2=0.075/4.9ms^2 so t =sqrt of 0.015 so t = 0.122seconds

i the put this value int0 s=ut+0.5at^2
so horizontally 20m=ux0.122+0.5(9.8ms^2x0.122^2)
=20=ux0.122+0.073 so 19.937/0.122 =u so u = 163ms^1

so the velocity on leaving the pistol was 163ms^1

second question.

A shot is fired with a velocity of 100ms^1 at an angle of 25degrees above a horizontal plane.Find...a) the time of flight on the horizontal plane b) the range on the horizontal plane. c)the greatest heiht the shot attains above the horizontal plane. d)the velocity of the shot (magnitude and direction)8.0seconds after it was fired.

for a i get 8.73 seconds b) i get 790metres c)i get 91m and d) i get 120ms^1 at 25degree to the hoizontal.

i am having a little bit of a job getting my head around this topic so if thes are not correct can someone help me out with what im doing wrong?

Kind regards,
Chris.

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Doc Al
Mentor
First question is..

A shot is fired horizontally at a target 20m away and it is notice3d that the bullet hits a point 7.5cm below the target aimed at. What was the velocity of the bullet when it left the pistol?

I get vertically
u=0ms^1 a=9.8ms^2 s=0.075m need t
so i used s=ut+0.5at^2
=0.075m=4.9t^2
t^2=0.075/4.9ms^2 so t =sqrt of 0.015 so t = 0.122seconds
So far, so good. Just be careful about how you round off your calculations. (Don't round off until the end.)

i the put this value int0 s=ut+0.5at^2
so horizontally 20m=ux0.122+0.5(9.8ms^2x0.122^2)
=20=ux0.122+0.073 so 19.937/0.122 =u so u = 163ms^1
Is the horizontal motion accelerated? (Which way does gravity act?)

second question.

hello, well the horizontal velocity is constant and g act downwards so only effects the vertical motion? i take it 163ms^1 is wrong.

sorry for not putting my working for the second question. Here it is

for question 2..
a)

V(horiz) = cos25degree x 100ms^1 so V(horiz) =90.6307787ms^1
V(vert)= sin25degrees x 100ms^1 so V(vert)=42.3ms^1

so taking the motion at max height
V=0
u=42.26182617^1
A=g=9.8ms^2 need t

so used V=u+AT
0=42.26182617 +9.8 x t
so t=42.26182617/9.8 = 4.32 seconds x 2 = 8.73seconds

b) i just did range = horizontal velocity x flight time
=90.6307787x8.73= 790m (3sf)

c) t=4.32seconds u=42.26182617ms^1 v=0ms^1 s=h
s=ut+0.5at^2
so = 42.26182617x4.32+0.5(-9.8x4.32^2)
=182.5710891-91.44576
h = 91.1253291 metres

d)at 8.0 sec g is acting at 78.4ms^2 downwards horizontal = constant 90.6307787ms^1
so resultant velocity = v^2 = 78.4^2 + 90.6307787ms^1^2
= 6146.56+8213.938048=v^2
V=sqrt of 14360.49805 = 119.8352955ms^1

to find the angle i used tan theta = 42.26182617/90.6307787 =tan-1 o.466307658=
25degrees

Hope you can help further, thankyou
Chris

Doc Al
Mentor
hello, well the horizontal velocity is constant and g act downwards so only effects the vertical motion? i take it 163ms^1 is wrong.
Yes, it's wrong.

sorry for not putting my working for the second question. Here it is

for question 2..
a)

V(horiz) = cos25degree x 100ms^1 so V(horiz) =90.6307787ms^1
V(vert)= sin25degrees x 100ms^1 so V(vert)=42.3ms^1

so taking the motion at max height
V=0
u=42.26182617^1
A=g=9.8ms^2 need t

so used V=u+AT
0=42.26182617 +9.8 x t
so t=42.26182617/9.8 = 4.32 seconds x 2 = 8.73seconds
Good. Except for that last step (x 2).

b) i just did range = horizontal velocity x flight time
=90.6307787x8.73= 790m (3sf)
Good. But correct the error propagated from part A.

c) t=4.32seconds u=42.26182617ms^1 v=0ms^1 s=h
s=ut+0.5at^2
so = 42.26182617x4.32+0.5(-9.8x4.32^2)
=182.5710891-91.44576
h = 91.1253291 metres
Good.

d)at 8.0 sec g is acting at 78.4ms^2 downwards horizontal = constant 90.6307787ms^1
so resultant velocity = v^2 = 78.4^2 + 90.6307787ms^1^2
= 6146.56+8213.938048=v^2
V=sqrt of 14360.49805 = 119.8352955ms^1
Redo this. What's the vertical component of velocity at 8 seconds? (g is always 9.8 m/s^2 downward.)

sorry didn't mean to put the g=78.4 bit that would be the vertical velocity at 8.0sec and the horizontal is 90.6... so whatdo i do with that i thought i would find the resultant and then find the angle using trig? on the time should i have just left a 4.32sec? i thought it would be timesd by 2 as it is only halfway through the motion?

Chris.

okat 4.23 sec the vert velocity is 0 as the object is at max height so at 8 sec i work out that the vert velocity = 36.946ms^1 (3.77 secs after attaing max height?)
is this correct?

Thankyou,
Chis.

Doc Al
Mentor
It's easier than all that. The vertical component of velocity is given by:
$$v = v_0 - gt$$

Just plug in the numbers:
$$v = 100\sin25 - (9.8)(8)$$

oh ok what is the v0 bit in that equation horizontal velocity? and for question 2 part a you said i was wrong to multiply the time of 4.23 seconds by two, how come? i thought this would be the max height reached so i thought i ha to multiply by 2 to get the total time of flight. Could you explain this for me as they did the same in my textbook?

Thankyou,
Chris.

Doc Al
Mentor
oh ok what is the v0 bit in that equation horizontal velocity?
In my last post, I used v0 to stand for initial velocity in the vertical direction.

and for question 2 part a you said i was wrong to multiply the time of 4.23 seconds by two, how come?
It wasn't wrong to multiply by two, you just made an error when you did. 4.32 x 2 = 8.64 (not 8.73 like you wrote).

Hello, i have just had a quick go at the first question i posted and is the answer 221.6ms-^1. I just did 300ms-^1sin90-g x t is this correct?

Thanks,
Chris.

Doc Al
Mentor
Hello, i have just had a quick go at the first question i posted and is the answer 221.6ms-^1. I just did 300ms-^1sin90-g x t is this correct?
Do you mean the first problem in your first post? If so, this isn't even close. (Your initial answer was very close, but your method was off a bit.)