Which one of the following equations is dimensionally
homogeneous? show your proof.
a. f = ma
b. f = m(v2/r)
c. f(t2 - t1) = m(v2 – v1)
d. f =mv
e. f = m(v2 – v1)/(t2 – t1)
where
f = force (n)
m = mass (kg)
a = acceleration (m/s2)
v = velocity (m/s)
r = radius (m)
t = time (s)

Explanation:

We need to calculate the equations is dimensionally  homogeneous.

We know that,

Unit of force is Newton.

Unit of mass is kg.

Unit of acceleration is m/s².

Unit of velocity is m/s.

Unit of radius is m.

Unit of time is sec.

(a). Given that,

Put the unit of all elements

Here,

This equations is dimensionally  homogeneous.

(b). Given that,

Put the  unit in the formula

This equations is dimensionally  homogeneous.

(c). Given that,

Put the  unit in the formula

This equations is dimensionally  homogeneous.

(d). Given that,

Put the  unit in the formula

This equations is not dimensionally  homogeneous.

(e). Given that,

Put the  unit in the formula

This equations is dimensionally  homogeneous.

Hence, This is required solution.

this would be about 43%

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.