Finding components of velocity

[homevolend]

Homework Statement

A hockey player shoots hockey puck towards net. The net is 20 metres infront of the player. If the puck leaves hockey stick at 30 m/s and 10° above ice. Find x and y components of the velocity. If the goalies catches puck just infront of net calculate final velocity of the puck with magnitude and direction included in answer.

Homework Equations

v_x = vcosθ
v_1y=vcosθ

3. The Attempt at a Solution [/b

Ok now for the first I assume it means find x and y components of the velocity means of the initial velocity.

so I did the above equations of

v_x = vcosθ
v_1y=vcosθ

and got: v_1y=5.2 m/s
and v_x=29.5 m/s


now for next part I did:

d_x=v_x(t)
20=29.5(t)
t=0.7 sec

v_2y=v_1y+(g)(t)
v_2y=5.2+(9.81)(0.7)
v_2y=12.1 m/s

v₂=√ 29.5²+12.1²
v₂=31.9 m/s

tan^-1(12.1/29.5)=θ
θ=22.3°

final velocity of the puck is 31.9 m/s [22.3° Forward]


Im just wondering if I did this question correctly and if my direction is correct for the final part.

 

[ehild]

v_x = vcosθ
v_1y=vcosθ

You wanted to write v_1y=vsinθ...

and got: v_1y=5.21 m/s
and v_x=29.5 m/s

Do not round too early, too much.

v_2y=v_1y+(g)(t)
v_2y=5.2+(9.81)(0.7)
v_2y=12.1 m/s

Reconsider the sign of v1y and g. One is up, the other is down. The result you got is wrong.

ehild

 

[homevolend]

Ok re did and got this for the x and y components

vx = vcosθ
v1y=vsinθ

v1y=5.21 m/s
and vx=29.54 m/s


now for next part I did:

dx=vx(t)
20=29.54(t)
t=0.677 sec

v2y=v1y+(g)(t)
v2y=5.21+(-9.81)(0.677)
v2y= -1.4 m/s

v2=√ 29.54²+(-1.4)²
v2=29.5 m/s

tan-1(-1.4/29.54)=θ
θ= what did I do wrong?

not sure what I did wrong

 

[ehild]

Do not round off during calculations. Keep at least 4 significant digits. The final angle will be negative as the puck is falling, its vertical component of velocity is negative.ehild

 

[rwisz]

Also, is there anything else I could have included in my solution?

Your solution looks correct. You correctly found the x and y components of the initial velocity and used them to calculate the time it takes for the puck to reach the net. Then, you used the equation for vertical motion to find the final vertical velocity and used the Pythagorean theorem to find the magnitude of the final velocity. Finally, you used the inverse tangent function to find the direction of the final velocity.

One thing you could have included is a diagram to better visualize the problem and your solution. You could also mention the units for each of your calculations, as well as the units for the final answer. Additionally, you could explain the significance of the angle of 10° above the ice in relation to the initial velocity. Overall, your solution is correct and includes all the necessary steps to solve the problem.