Is the Kinematic Equation Applicable for Calculating Projectile Motion Speed?

[mybrohshi5]

Homework Statement

Firemen are shooting a stream of water at a burning building using a high-pressure hose that shoots out the water with a speed of 27.5 m/s as it leaves the end of the hose. Once it leaves the hose, the water moves in projectile motion. The firemen adjust the angle of elevation Θ of the hose until the water takes 3.00 s to reach a building 51.81 m away. You can ignore air resistance; assume that the end of the hose is at ground level.

How fast is it moving just before it hits the building?

Θ=51.1

Homework Equations

The equation i used to solve it was V=sqrt(v_x²+v_y²) and the answer was found to be 19.0 m/s

i was wondering if this equation would work to solve it? i can't get it to come out with 19 m/s though.

V_f²= V_yi²+2(a_y)(Δy)

The Attempt at a Solution

V_f²= V_yi²+2(a_y)(Δy)

so with this equation i used V_yi to be 27.5sin(51.1)=21.01

i used a_y to be -9.8

i used Δy to be 27.5sin(51.1)(3) + .5(-9.8)(3²) = 20.11 - 0 = 20.11
(the minus 0 is because of the final height minus the initial height).V_f²= V_yi²+2(a_y)(Δy)

V_f = 6.87 which is definitely wrong.

Anyone know why this equation doesn't work using these numbers i calculated?

Any suggestions. Thanks :)

 

[Doc Al]

i was wondering if this equation would work to solve it? i can't get it to come out with 19 m/s though.

V_f²= V_yi²+2(a_y)(Δy)

That will find V_yf, not the complete V_f. You still need to add V_x to get the total V.

 

[mybrohshi5]

if i add that to the Vx then that comes out to be 24.14 m/s which is also not the correct answer.

6.87 + 27.5cos(51.1) = 24.14 m/s

 

[Doc Al]

if i add that to the Vx then that comes out to be 24.14 m/s which is also not the correct answer.

6.87 + 27.5cos(51.1) = 24.14 m/s

These are vector components. When I said 'add' I meant combine them like vectors:

V=sqrt(v_x²+v_y²)

 

[mybrohshi5]

oh i see what you are saying.

well i did that and its still a little under

sqrt(17.27^2 + 6.87^2) = 18.58 :(

i guess this way may just not work.

Thank you for your help and explanations.

 

[Doc Al]

i guess this way may just not work.

It should work just fine. Check your arithmetic. For example, this calculation is not quite right:

so with this equation i used V_yi to be 27.5sin(51.1)=21.01

 

[mybrohshi5]

thank you. with that new number of 21.4 it works out correctly.

thank you for catching that error and all of your time and help :)