One type of bb gun uses a spring-driven plunger to blow the bb from its barrel. (a) calculate the force constant of its plunger's spring if you must compress it 0.150 m to drive the 0.0500-kg plunger to a top speed of 20.0 m/s. (b) what force must be exerted to compress the spring?

using energy conservation equation,

a) 0.5*kx^2 = 0.5 mv^2

0.5 * K * (0.150)^2 = 0.5 * 0.0500 * 20^2

0.01125K = 10

K = 888.8889 N/m

b)

force = kx = 888.8889 * 0.150 = 133.3333 N

 

Ireally don’t know

Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.