i need help with these physics questions?

Question

A baseball is hit off a 1 meter high tee at an angle of degrees and at a speed of m/s. How far to the nearest tenth of a meter does it travel horizontally?

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2
A golf ball is chipped at an angle of degrees and with a speed of m/s how far does it travel to the nearest tenth of a meter?

A monkey swings on a vine and at the bottom of the swing while moving horizontally lets go of the vine aiming for another vine meters away horizontally and whose bottom is meters below the monkey. How fast must the monkey be moving to the nearest tenth of a m/s in order that he just catches the bottom of the vine?

Answer 1

1. Angle of th and speed of v
y(t)=1+v*sin(th)*t-.5*g*t^2

The ball will impact the ground when y(t)=0
0=1+v*sin(th)*t-.5*g*t^2
solve for t (the positive root) and plug it into
x(t)=v*cos(th)*t to find the range.

2. Angle of th and speed of v
y(t)=v*sin(th)*t-.5*g*t^2

The ball will impact the ground when y(t)=0
0=v*sin(th)*t-.5*g*t^2
note that t=0 is a solution
the t for the range is
t=2*v*sin(th)/g
plug it into
x(t)=v*cos(th)*t to find the range.

3) for the monkey, if the vine is d meters away and s meters below when releasing at a speed of v
y(t)=-.5*g*t^2
and
x(t)=v*t

in order to catch the bottom of the vine, when
y(t)=-s
and
x(t)=d

then
d=v*t
s=.5*g*t^2

solve for v

v=d*sqrt(g/(2*s))

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