Q:1 A motorist traveling with a constant speed of 15 m/s (about 34 mi/h) passes a school-crossing corner, where the speed limit is 0 m/s (about 22 mi/h). Just as the motorist passes, a police officer on a motorcycle stopped at the comer starts off in pursuit with constant acceleration of 3.0 m/S2. (a) How much time elapses before the officer catches up with the motorist? (b) What is the officer's speed at that point? (c) What is the total distance each vehicle has traveled at that point? Q:2A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.350s. ignore air resistance. Find (a) the height of the tabletop above the floor; (b) the horizontal distance from the edge of the table to the point where the book strikes the floor; (c) the horizontal and vertical components of the book's velocity, and the magnitude and direction of its velocity, just before the book reaches the floor. Q:2Determine the Resultant = R and Angle = Ø of given Vectors by using Component method.
Answers
Explanation:
Given A motorist traveling with a constant speed of 15 m/s (about 34 mi/h) passes a school-crossing corner, where the speed limit is 0 m/s (about 22 mi/h). Just as the motorist passes, a police officer on a motorcycle stopped at the comer starts off in pursuit with constant acceleration of 3.0 m/S2. (a) How much time elapses before the officer catches up with the motorist? (b) What is the officer's speed at that point? (c) What is the total distance each vehicle has travelled at that point? A physics book slides off a horizontal tabletop with a speed of 1.10 m/s. It strikes the floor in 0.350 s. ignore air resistance. Find (a) the height of the tabletop above the floor; (b) the horizontal distance from the edge of the table to the point where the book strikes the floor; (c) the horizontal and vertical components of the book's velocity, and the magnitude and direction of its velocity, just before the book reaches the floor. Q:2 Determine the Resultant = R and Angle = Ø of given Vectors by using Component method.Now distance = velocity for the police officer and when the police catches up with the motorist.
- So x (police) = 0, vel (police) = 0 and acceleration(Police) = 3 m/s^2
- Now x (motorist) = 0, vel(motorist) = 15 m/s, accn(mo) = 0
- We need to find when police and motorist are at same location. (P = M)
- So v x t = ½ a t^2
- 15 x t = ½ x 3 x t^2
- 15 = 3t / 2
- 3t = 30
- Or t = 10 secs
- Now we have
- V = u + at
- = 0 + 3 x 10
- Or V = 30 m/s
- So distance s1 = s2
- = v x t
- = 15 x 10
- = 150 m
- So we need to find the height of the table top. So we have
- So Δy = V (ini) t + ½ gt^2
- = 0 + ½ x – 9.81 x 0.35 x 0.35
- So y = - 0.600 m
- Or y = 0.6 m
- Now for the horizontal distance we have
- So Δx = V (ini)t + ½ at^2
- = (1.1) x 0.35 + ½ x 0 x t^2
- = 0.385 m
- Now for the third part we have
- Velocity V = 1.1 m/s
- So Vy = Vo y + at
- = 0 + (- 9.81 x 0.35)
- = - 3.43 m /s
- So velocity = magnitude
- So V = √Vxy^2 + Vy^2
- = 3.6 m/s
- So angle theta = tan^-1(-3.3 / 1.1)
- = - 72.2 degree
Answer: (a)t= 10s,(b)V= 30m/s,(c)S=150m.
Explanation: For the officer to catch up then S1 has to be equal to S2,S1 =vt for the motorist,S2=vi+½at² where vi=0.therefore,S2=½at². So vt=½at²
vt-½at²=0,<=>t(v-½at)=0,
t=0,v-½at=0,
15-½(3.0)t=0,=> 15=1.5t,=>15/1.5=1.5t/1.5
t=10s. (b) v=vi+at=>0+(3.0)(10)=30m/s.
(c) s=½at²=½(3.0)(10)²=150m.