43. a rocket sled accelerates at a rate of 49.0m/s2. its passenger has a mass of 75.0 kg. (a) calculate the horizontal component of the force the seat exerts against his body. compare this with his weight using a ratio. (b) calculate the direction and magnitude of the total force the seat exerts against his body.

(a) 3675 N

Assuming that the acceleration of the rocket is in the horizontal direction, we can use Newton's second law to solve this part:

where

is the horizontal component of the force

m is the mass of the passenger

is the horizontal component of the acceleration

Here we have

m = 75.0 kg

Substituting,

(b) 3748 N, 11.3 degrees above horizontal

In this part, we also have to take into account the forces acting along the vertical direction. In fact, the seat exerts a reaction force (R) which is equal in magnitude and opposite in direction to the weight of the passenger:

where we used

as acceleration of gravity.

So, this is the vertical component of the force exerted by the seat on the passenger:

and therefore the magnitude of the net force is

And the direction is given by