A200 g hockey puck is launched up a metal ramp that is inclined at a 30° angle. the coefficients of static and kinetic friction between the hockey puck and the metal ramp are μs = 0.40 and μk = 0.30, respectively. the puck's initial speed is 93 m/s. what vertical height does the puck reach above its starting point?

the vertical height reached by the puck is 580.47 m

Explanation:

given,

mass of hockey puck = 200 g

angle of inclination (θ )= 30°

μs = 0.40                                      

μk = 0.30                                

initial velocity = 93 m/s

acceleration of pluck upwards,

a = - g (cosθ ×  μk +sin θ)                              

a = - 9.81 × (0.3 × cos 30°  +sin 30°)

a = -7.45 m/s²

now,                                    

s =

s =

s = 580.47 m

the vertical height reached by the puck is 580.47 m

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.