Answer:
2.42 seconds
Explanation:
Assume that air resistance is negligible, use trigonometry to find the vertical component of the velocity by using trigonometry:
<span>31⋅<span>sin50</span>=23.7</span>
Where 31 <span>m<span>s<span>−1</span></span></span> is the hypotenuse and by using sin to get the opposite component (vertical velocity) of the trajectory.
Now comes the use of the formula:
v = u + at
where v is the final velocity (0 <span>m<span>s<span>−1</span></span></span>), u is the initial velocity (31 <span>m<span>s<span>−1</span></span></span> ), a is the acceleration of gravity (9.81 <span>m<span>s<span>−2</span></span></span>) and t is the time it takes to arrive at the top of the trajectory.
By making t as the subject:
<span>t=<span><span>v−u</span>a</span></span>
You can calculate the value of t:
<span><span><span>0−23.7</span><span>−9.81</span></span>=2.42</span> (to 3 significant figures)
Better way to see it:
<span><span><span>0−<span>(31⋅<span>sin50</span>)</span></span><span>−9.81</span></span>=2.421</span> (to 4 significant figures)
Note: You must remember that you are dealing with velocity, not speed . Since velocity is a vector quantity, you must select the direction at which values will be positive. In my example, I set my upward direction as the positive value while my downward vectors as negative value (a, acceleration, 9.81 <span>m<span>s<span>−1</span></span></span>).
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Hope this helps,
kwrob