Answer:
Option b) 17.3 m/s and 5.10 m
Explanation:
For this case, we can consider a parabolic shot, for which we have an initial speed of 20 m/s, which has a vertical component (Voy) and a horizontal component (Vox) - see attached picture 1 on this case -
According to the figure, we have a right rectangle, for which we can obtain the following formulas:
V₀ₓ= V₀Cosα
V₀y=V₀Senα
With these formulas, we can first obtain the horizontal component of velocity:
V₀x=20xCos30= 17.32 m/s
Then we need to obtain the maximum height (point C on the chart). At this point, we can think about a freefall, where speed is given by :
V=gt , where g= gravity acceleration and t=time
Our maximun time at point C will be: tmax=V/t, and we can replace vertical component of speed, given by V₀Senα, then:
Tmax=V₀Senα/g
Finally, if we still consider a movement in free fall, time is given by :
t= √(2h/g) then h=(gt²)/2 and replacing our time previously found:
hmax=(V₀xsenα)²/2g
And replacing our numbers: hmax= 5.10 m
