Homework SourseGertrude is aiming a super Drencher water pistol at Egbert w
Gertrude is aiming a super Drencher water pistol at Egbert, who is 1.6 m tall and is standing 5 m away. Gertrude holds the water gun 1 m above ground at an angle (alpha) of elevation.
a)
if the water pistol fires with an initial speed of 7m/sec and an elevation angle of 45 degrees, does Egbert get wet?
b)
if the water pistol fires with an initial speed of 8 m/sec, what posssible angles of elevation will cause Egbert to get wet?
a)
if the water pistol fires with an initial speed of 7m/sec and an elevation angle of 45 degrees, does Egbert get wet?
b)
if the water pistol fires with an initial speed of 8 m/sec, what posssible angles of elevation will cause Egbert to get wet?
Solution
a)R at height 1m
R=u^2 sin2alpha/g
=49*1/2*9.8=5
hence it strikes him at height 1m so he gets wet
b)y=xtanalpha-.5gx^2/U^2cos^2alpha
put x=5 in this eqn n differentiate y with respect to alpha to get maximum y at 5m.
you get alpha=52.5m
therefore y1 at this y=1.35m
therefore total y=1.35+1=2.35m which goes above men so it doesnt make him wet
put y=.6 and x=5 in above eqn and calculate respective alpha
.6=5tanalpha-.5*9.8*25(1+tan^2alpha)/64
we get alpha=34 and 62
therefore between 34 and 62 water goes above the man.
now putting y=-1 and x=5 in above equation similarly
we get alpha=5.7degree and 70 degree
therefore alpha belongs to (5.7,34) U (62,70)
which is the required answer :)
