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__Question 1:__

A catapult on a cliff launches a large round rock towards a ship on

the ocean below. The rock leaves the catapult from a height H of 32.0 m above sea level, directed at an angle above the horizontal with an unknown speed v0. The projectile remains in flight for 6.00 seconds and travels a horizontal distance D of 160 m. Assuming that air friction can be neglected,

A. calculate the value of the angle (in degrees).

B. Calculate the speed at which the rock is launched.

I've looked at similar questions posted on this forum, but I am still unsuccessful at getting the answer.

Relevant Equations:

X = Xo+ Vot+.5at^2

V=Vo+at

V^2= Vo^2 + 2a (X-Xo)

Okay, here is what I have done:

A. x = xo + vixt + 1/2at^2

160 = vix(6.00) + (1/2)(-9.81)(6.00)^2

vix=56.1m/s

y=yo + viyt + 1/2at^2

-32 = viy(6.00) + (1/2)(-9.81)(6.00)^2

viy=24.1

theta = 24.1/56.1tan^-1 = 23.2 deg

but the answer says it should be 42.1 deg, i don't know where i am making my mistake?

B. (viy)^2 + (vix)^2 = (vi)^2

SQRT((56.1)^2 + (24.1)^2) = 61.0m/s

but the answer should be 35.9m/s, again i cant find my mistake.

__Question 2:__

A wind is blowing directly from east to west. The pilot of a small plane finds that if he points the nose of the plane 28.4 ° north of east, his velocity with respect to the ground is in the direction 56.7 ° north of east. The speed of the plane with respect to the air is 129 m/s.

A. Taking North to be the y-direction and East to be the x-direction, what is the y-component of plane's velocity with respect to the ground?

B. What is the magnitude of the plane's velocity with respect to the ground?

Relevant Equations:

I don't know, haha, no idea where to go with this problem

What I did:

I really don't know what to do with this one, I tried drawing a diagram but that didn't really help me out.

Any help would really be appreciated!