Physics geeks1?

Question

A boy on a skate board skates off a horizontal bench 5 m heigh at a speed of 10m/s. the speed(m/s)and the magnitude of acceleration(m/s^2)respectively,immediately before he touches the floor are?

Answer 1

If we ignore air friction, the horizontal component of speed will remain the same.

The boy will gain kinetic energy equal to the vertical drop:
m*g*h=.5*m*v^2

this will be the vertical component downward

v=sqrt(2*g*h)
=sqrt(2*9.81*5)
9.9 m/s

the magnitude of the velocity is

sqrt(9.9^2+10^2)
14 m/s
the direction is
atan(10/9.9) downward from horizontal

45. 3 degrees

j

Answer 2

split into horizontal and vertical motions.

in the horizontal direction. speed = 10 m/s and acceleration = 0 before leaving the bench and immediately prior to hitting the floor. speed in horizontal direction is not effected by falling..

in up and down direction (call it x)

accelaration = 9.8 m/s^2 (same as acceleration due to gravity

and velocity if found by

Vf ^2= Vi^2 + 2 a x

where
Vf = velocity final (ie velocity as object hits floor)
Vi = 0 (since skate board is traveling only horizontally and not up and down)
a = 9.8 m/s^2
x = 5 m

Vf^2 = 0 + 2 * 9.8m/s^2 * 5m = 98 m^2/s^2

solve for Vf

you do the rest....

Answer 3

Well, I think the first solution is wrong, why is that ?

you said the the skate is on a benche 5 m height, so it's kind of a plane inclinade, we need to use the conservation of energy, yes that's it :

Initial energy = m*g*5 + m*100 / 2

Final energy = m*v^2/2

m*g*5 + m*100 / 2 = m*v^2 / 2

g = 10 m/s^2

50 + 50 = v^2 / 2

v = 10*sqrt(2) m/s

The acceleration :

Force = mass*acceleration

The plane inclinade makes an angle with the horizontal : theta

mg*sen(theta) = m*a

a = g*sen(theta) m/s^2

Hope thath helped you

Answer 4

well assuming that there is no friction, and you want the vertical acceleration, and vertical velocity, the acceleration would be gravity (-9.8 m/s^2) and velocity should be about 9.9 m/s using the formula Vf^2 = Vi^2 + 2ad.....Vf is ur unknown, Vi is 0, a is 9.8, and d is 5