Batpenguin sees the penguinsignal and leaps into the penguinmobile, which is at rest in the icy penguincave on a smooth

[answerhappygod]

Batpenguin sees the penguinsignal and leaps into the
penguinmobile, which is at rest in the icy penguincave on a smooth
and unsloped slippery floor with static friction coefficient μS​=
0.2.
1. The penguinmobile has a mass of m = 1.3x10^2kg and the
penguincave is just beneath the surface of the Earth with
gravitational acceleration downward at g 9.8 m/s^2. Batpenguin
wants to accelerate as fast as possible to get to the scene of the
crime, but doesn't want to slip on the icy floor. What is the
maximum force (in Newtons) that the bottoms of the wheels can exert
on the ground to push the car forward without slipping when
Batpenguin stomps on the accelerator?
2. What is the maximum acceleration of the penguinmobile (in
m/s^2) that Batpenguin can achieve without the wheels slipping?
3. The road out of the penguincave is L = 100 m long and flat
until the very end, where there is the start to a ramp up to a jump
across the penguinmoat. From experience, Batpenguin knows that she
needs the penguinmobile to be traveling at least 18 m/s at the
bottom of the ramp in order to make the jump. If the penguinmobile
keeps constant maximum acceleration (before slipping as in the
previous problem) for the entire 100 m road, will Batpenguin make
the jump? (True = Yes, False = No. Assume the penguinmobile is so
slick and advanced that it does not experience drag from air
resistance. Explain your answer in the write-up.) (T/F)
4. After traveling the full 100 m length at constant
acceleration, Batpenguin reaches the bottom of the ramp, which
tilts up from the horizontal. While going up the ramp Batpenguin
notices that despite having the same constant acceleration forward
(parallel to the ramp), the speed of the car is also remaining
constant while on the ramp. By what angle (in radians) must the
ramp be tilted upwards for this to be true?