Help with a Physics question please

MoonDancer

I'm doing some revision and I'm stuck on a question:

A launcher located at the edge of a 30 m cliff is used to fire a projectile directly upwards
with an initial speed of 10 m/s. The projectile reaches a maximum height and then falls to the ground at the bottom of the cliff.

Calculate the time taken for the projectile to complete its journey from the launcher to the bottom of the cliff.
(Use g = 9.81 m/s2. You may neglect air resistance and assume level ground)

Help greatly appreciated

First find how long it takes to reach its maximum height (t_1). At this height, its velocity in the y direction is zero.

v_y = u_y + a_y*t_1 ---> 0=10 -9.81*t_1 ---> t_1=10/9.81= 1.02s

The distance traveled in the y direction in this time is:

s_y = u_y*t_1 + 0.5*a_y*(t_1^2) --> s_y= 10*1.02 - 0.5*9.8*(1.02^2) --> s_y = 5.1m

Next, calculate the time taken to reach the ground from its maximum height (t_2), i.e. the time taken for it to fall a height of 30m+5.1m = 35.1m. Once again at this height its velocity in the y direction, which is now its initial velocity, is zero.

s_y = u_y*t_2 + 0.5*a_y*(t_2^2) --> 35.1 = 0.5*9.8*(t_2^2) --> t_2 = sqrt(35.1/0.5*9.8) ---> t_2 = 26.23s.

Hence the total time is t_1 + t_2 = 1.02s + 26.23s ---> t= 27.25s.

MoonDancer

Thanks so much, so in other words, I just rearrange the dynamics equation: v=u+at to get t=u/v+a

Then s=ut+1/2at^2 to get me the distance, and rearranged again to get the time.

Thanks for the help, it's so simple when you think about it ugh.

MoonDancer

Deleted User wrote: »

s_y = u_y*t_2 + 0.5*a_y*(t_2^2) --> 35.1 = 0.5*9.8*(t_2^2) --> t_2 = sqrt(35.1/0.5*9.8) ---> t_2 = 26.23s.

Hence the total time is t_1 + t_2 = 1.02s + 26.23s ---> t= 27.25s.

I'm not getting that answer, I'm keying in squareroot of 35.1/(0.5)(9.81) and getting 2.68 What am I doing wrong?

Jaysus that's a feckin tricky one.

MoonDancer

MoonDancer wrote: »

I'm not getting that answer, I'm keying in squareroot of 35.1/(0.5)(9.81) and getting 2.68 What am I doing wrong?

Jaysus that's a feckin tricky one.

You're probably right. I wrote all of that on my phone so I wouldn't be surprised if there's a numerical error here or there.

Ciaran

MoonDancer wrote: »

I'm not getting that answer, I'm keying in squareroot of 35.1/(0.5)(9.81) and getting 2.68 What am I doing wrong?

Jaysus that's a feckin tricky one.

You have it right, Aristotle multiplied by 9.81 instead of dividing. The perils of missing brackets.

MoonDancer

Thanks for all the help, those questions really get me, must keep practicing.