Calculating Velocity of Bullet at Ground Impact

[theuniverse]

Homework Statement

A bullet is fired from a cliff 36m above the ground. If the bullet is fired at an angle of 25 above the horizontal, and has a muzzle velocity of 80m/s, what is the velocity of the bullet as it hits the ground?

d = 36m
vi = 80m/s
angle = 25 degrees

Homework Equations

The Attempt at a Solution

Horizontal: 80 cos 25 = 72.5

Vertical: muzzle: 80 sin 25 = 33.8

0^2 = 33.8^2+2ad <-- Top of the projectile motion
0= 1142.44+2(-9.8)d
d= 1142.44/19.6
d= 58.28

height = 58.28+36 = 94.28
Vf^2= vi^2+2ad <-- Top of the parabola = 0m/s
vf^2= 2ad
vf^2= 2(9.8)(94.28)
Vf^2= 1847.88
Vf= 42.99
R^2 = 42.99^2+72.5^2 = 7105.25
R = 84.3

I was just wondering if I did it right...

Thank you very much,

 

[Doc Al]

Looks good to me, but you could have calculated the change in vertical speed in one step using the same formula (Vf^2 = Vi^2+2ad). Let a = -9.8 m/s^2 and d = -36 m.

(You could also have used conservation of energy.)

 

[nlightner]

your calculations seem to be correct. However, it is important to note that the velocity of the bullet as it hits the ground will depend on the air resistance and other factors. These calculations assume ideal conditions and may not be 100% accurate in real-life situations. It is always important to take into account all variables and factors when conducting scientific calculations.