Question

7. The nearest star is 4.1 x 1016 m away. Suppose you had a spaceship that could accelerate from rest at 10 m/s? for half a year, then continues at constant speed. How long would it take to reach the nearest star? Use 1 year 365 days, 24 hours -1 day, 60 minutes 1 hour, 60 seconds 1 minute. も. 15768111 vA: at 2 1.24 16 15 구 68 oooo 8. A roofer on the ground throws a hammer to another roofer who is higher up or the roof of a house. The initial velocity of the hammer is 12 m/s at an angle of 78° above horizontal. At the instant the hammer is caught, it is traveling horizontally, so its vertical speed is zero. What is the vertical height between the two roofers? rts Page 3 of 4

Answer 1

7) distance covered in half a year

S = ut + 0.5at^2

S = 0 + 0.5*10*(365*24*60*60/2)^2

   = 1.24*10^15 m

distance remains = (4.16*10^16 - 1.24*10^15) = 4*10^16 m

speed at the end of half year

v = u + at

= 0 + 10*(365*24*60*60 / 2)

= 1.5768*10^7 m/s

time taken = distance / speed = 4*10^16 / 1.5768*10^7 = 2536783358.7 s = 80.44 years

total time taken = 80.44 + 0.5 = 80.94 years

8) since the vertical speed is zero , it is at the maximum height

using the equation of linear motion we have

vy^2 - uy^2 = 2gH

0 - (12 sin 78)^2 = 2*-9.8*H

H = 7.03 m

so the vertical height between the two roofers is 7.m