1.) Find the angle(in degrees) that A+B vector makes on the x-axis. A=5i+2j-k B=

Question

1.) Find the angle(in degrees) that A+B vector makes on the x-axis.

A=5i+2j-k

B=-i+j+k

2.) An automoble traveling along a straight road increases its speed from 30 m/s to 50m/s in a distance of 180m. If the acceleration is constant, how much time elapses while the auto moves this disance.

3.) An electron starting from rest and moving with a constant acceleration , travels 2 cm in 5 ms. What is the magnitude of acceleration?

4.) A dart is thrown horizontal toward x at 20m/s as shown. It hits Y 0.1s later. The distance XY is?

Explanation / Answer

2.

Let : d = 180 m

vi = 30 m/s,

and vf = 50 m/s.

The distance is d = vav t = {(vi + vf) / 2 }*t

t = 2 d / (vi + vf ) = 2*180m / (30m/s + 50m/s)

t = 4.5 sec

3.solution

  distance = initalspeed* time + 0.5*acceleration*time^2
d = ut + 0.5at2
u = 0 as the electron started from rest
therefore
d = 0.5at2
2.0cm in km = 2.0 x10-5, 5ms in seconds = 0.005
hence
2.0x 10-5 = 0.5 a 0.0052
a = 1.6 km/s2

4.solution

In the vertical direction, you have
y= y0 + vy0*t +ay0*t^2 = 0 + 0 -1/2*g*t^2
so the final change in height, which is y(0.1), is
XY = y(0.27) = -1/2* 9.8m/sec^2 * (0.1sec)^2
XY = 0.049 meters

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