What was the one with the uniform and radial gravitational fields
Q31, compare the maximum height reached by a vertically launched projectile under the two different assumptions.
Assumption A - constant (uniform) gravitational field.
g=9.8 m/s^2 and potential energy
U = mgh.
Assumption B - (downward) gravitational acceleration is
and potential energy is
Qualitative answer.
g is just the point value of GM/r^2 at the Earth's surface (r = 6380x10^3 m), but an over estimate for higher elevations. This means that assumption A will generally under estimate the maximum elevation, as it over estimates the strength of the gravitational field at higher elevations.
Quantitative answer.
Equate changes in PE (U) to the initial KE,
)
to obtain a formula for the max height under each assumption.
A :
B:
^{-1} - r_0)
Not really sure how much of a quntatitve answer they will want here? The equation for B is a bit unwieldy, it can be algebraically simplified a little bit more, but still not easy to tell by cursory inspection that it's even an approximation to the equation of A (well technically A is an approx of B). If you sub in some numbers however then you'll see they are a close approximation. For u<100 m/s the maximum height reached will be very similar for both. At u>1000 m/s however, you'll notice some significant under estimates in equation A.
the multiple choice was way harder this time