Honors Physics Question?

Question

If I could get any help with any of these questions, it would be much appreciated. These deal with projectiles and vertical/horizontal displacement.

1) The peregrin falcon flies at speed of 200 mph. Assume it moves horizontally at this speed 100 m above the ground when it brings its wings into its sides and freefalls. How far will the bird fall vertically while traveling horizontally a distance of 100 m? (Answer: 6.13 m just need work, please)

2) A puma jumps to a height of 12 feet when leaving the ground at an angle of 45 degrees. With what speed must it leave the ground to reach this height? (Answer: 12 m/s work or rational behind it needed)

Again, any help would greatly be appreciated! Thanks in advance.

Answer 1

1. convert mph to meters per second
1 mph = 0.44704 meters per second
vx=200*0.447
x(t)=200*0.447*t
solve for t when x(t)=100
t=1/(2*0.447)

the vertical fall distance will be
y(t)=.5*g*t^2
=6.137 m

2. convert feet to meters
1 foot = 0.305 meters

the flight to apogee is governed by energy
.5*m*vi^2=.5*m*(vi*cos(45))^2+m*g*12*0.305
vi^2=2*g*12*0.305/(1-cos^2(45))
vi= 12 m/s

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