To answer this problem we will make use of two of
the equations of motion. Then we will come across out each velocity component.
The difficult part comes in solving for the j component of velocity for which
we will have to know t_f, the time it takes to be displaced (11m):<span>
Our equations
1. v_f^2 = v_0^2 + 2ax </span>
<span>
2. v_f = v_0 + at
<span>Solving for the time it takes to travel 11m</span></span>
<span><span>
We do so by finding the final velocity using (1), and then
plugging that back into (2). </span></span>
<span><span>
v_fi^2 = 4^2 + 2*5*11 </span></span>
<span><span>
<span>v_fi^2 = 16 + 110 = 126</span></span></span>
<span><span><span>
v_fi = 11.22 m/s ((())) </span></span></span>
<span><span><span>
plugging this into (2) </span></span></span>
<span><span><span>
11.22 = 4 + 5*t_f </span></span></span>
<span><span><span>
5*t _f= 7.22</span></span></span>
<span><span><span>
t_f = 7.22 / 5 </span></span></span>
<span><span><span>
t_f = 1.444 seconds </span></span></span>
<span><span><span>
Solving for the vertical velocity </span></span></span>
<span><span><span>
v_fj = v_0j + at </span></span></span>
<span><span><span>
v_fj = 0 + 7*1.444 </span></span></span>
<span><span><span>
v_fj = 10.108 m/s ((())) </span></span></span>
<span><span><span>
Finding magnitude and angle </span></span></span>
<span><span><span>
V = sqrt(v_fi^2 + v_fj^2) </span></span></span>
<span><span><span>
</span></span></span>
125.884 + 10.108
V = 15.10151 m/s
<span>
Angle:</span>
<span>
Theta = arctan(v_fj/v_fi) </span>
<span>
<span>Theta = 0.0801 radians </span></span>
<span>
converting radians to degrees (180/pi) </span>
<span>
Theta = .0.0801(180/pi) deg= 4.591 deg </span>
<span>
Answer: </span>
<span>
V = 15.10151 m/s </span>
<span>
<span>Theta = 4.591 deg</span></span>
