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pooface
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Homework Statement
two problems. i am confused about their processes. they are almost the same but some things look strange.
problem 1:
A cannon on a level plain is aimed 50deg above the horizontal and a shell is fired with a muzzle velocity of 360m/s toward a vertical cliff 950 m away. how far above the bottom does the shell strike the side wall of the cliff?
problem 2:
A world series batter hits a home run ball with a velocity of 40m/s at an angle of 26deg above the horizontal. A fielder who has a reach of 2.2m above the ground is backed up against the bleacher wall which is 120 m from home plate. The ball was 1 m above the ground when it was hit. How high above the fielders glove does the ball pass?
Homework Equations
the kinematic equations.
The Attempt at a Solution
problem 1:
Vox=360cos50deg=231.403m/s
Voy=360sin50deg=275.78m/s
time of flight to the cliff
x=Voxt
950m=231.403t
t=4.1054s
final vertical velocity at impact with cliff
Vfy=Voy+ay*t
=275.78+(-9.81)*(4.1054)
=235.51m/s
QUESTION: This Vfy is a positive number. Does this mean that the shell is still rising at this point? Had there not been a cliff it would have gone higher passed this point right?
Height of the point of impact:
Vf^2=Vo^2 +2aS
Here i put Vf^2=0 because i want the displacement from the point of impact to the ground where Vf will be 0. and Vo will be the Vfy of the last step.
a=-9.81m/s^2
and the answer i get is 2.827km
PROBLEM 2:
Vox=40cos26=35.952m/s
Voy=40sin26=17.5348m/s
Time of impact with bleacher wall
x=Voxt
t=3.3378secs
final vertical velocity at impact with bleacher
Vfy=Voy+ay*t
=17.5348+(-9.81)(3.3378)
=-15.21m/s
QUESTION: I get a negative value here. Does this mean that the ball is descending?
Height of the point of impact:
Vf^2=Vo^2 +2aS
Here i put Vf^2=0 because i want the displacement from the point of impact to the ground where Vf will be 0. and Vo will be the Vfy of the last step.
a=-9.81m/s^2
and the answer i get is 11.7912m.
11.7912 - (2.2-1) = 10.5912m
Can someone see if I have done these questions correctly? thank you for your time.