Can you answer one of these physics questions?

Question

1)if A =12i-16j and B = -24i+10j, what is the magnitude of the vector C = 2A -B ?

a. 42

b. 22

c. 64

d. 90

e. 13

2)If A = 12i-16j and B = -24i+10j, what is the direction of the vector C = 2A - B ?

a. -49 degrees

b. -41 degrees

c. -90 degrees

d. 49 degrees

e. 21 degrees

A particle starts from the origin at t=0 with a velocity of 8.0j m/s and moves in th xy plane with a constant acceleration of (4.0i + 2.0j) m/s^2. at the instant the x coordinate of the particle is 29m, what is the value of its y coordinate?

a. 35m

b. 39m

c. 45m

d. 42m

e. 29m

Answer 1

1)

A = 12 i - 16 j

2A = 24 i - 32 j

B = -24 i + 10 j

C = 2A - B = (24 + 24) i + (-32 - 10) j

C = 48 i - 42 j

|C| = sqrt(48² + 42²)

|C| = 63.78

2)

tanα = 48/42 = 8/7

α = 48.81°

3)

Displacement equations:

x = (1/2)4 t² = 2t²

y = (1/2)2 t² + 8 t = t² + 8t

If x = 29

t = sqrt(x/2) = sqrt14.5

y = 14.5 + 8sqrt14.5

y = 44.96