Question

15) The momentum p of an object is equal to p = my where m is the mass of the object and is its velocity. If a car has a momentum and velocity given below? Determine the mass of the car using two methods 1) using the dot product and 2) using the magnitude of the vectors. p= (-35,238 kg m/s )X + ( 12,826 kg m/s 19 v = (-23.5 m/s ) + ( 8.56 m/s ) 16) Two position vectors are given below, what is the angle between the vectors? 71 = (+2 m )X + (+3 m ) + (-2 m )2 72 = (-1.5 m )X + (+3 m )) + (-2 m )2

Answer 1

15)

a) using dot product methode

p = mv

here x component of momentum

px = -35238 = m(-23.5)

m = 1499.5 kg

py = 12826 = m(8.56)

m = 1499 kg

b) using magnitude

m = p/v

m = 37500/25.01 = 1499.4 kg

16)

the dot product of r1 and r2

r1.r2 = 2(-1.5)+3*3+2*2 = 10

magnitude

r1 = sqrt(2^2+3^2+2^2) = 4.123m

r2 = sqrt(1.5^2+3^2+2^2) = 3.905

theta = cos^-1(10/4.123*3.905) = 51.6 degrees