An object's position in a given coordinate system is described by the vector r = t2 i - (3t + 3) j. assume the object moves without air resistance. einaaa@berkeley. edu 25%

part (a) what is the object's displacement between times t1 = 1 s and t2 = 3 s? write your answer in component form. δr = 8 i - 6 j ✔ correct!

The object´s displacement vector is Δr =  8i - 6 j  

Explanation:

Hi there!

The position vector is given by the following function:

r = t²i - (3t + 3) j

Let´s find the position of the object at time t1 and t2:

At t1 = 1 s:

r1 = (1)² i - (3 · (1) + 3 )j

r1 = 1 i - 6 j

At t2 = 3 s:

r2 = (3)² i - (3 · (3) + 3) j

r2 = 9 i - 12 j

The displacement is calculated as follows:

displacement = Δr = final position - initial position = r2 - r1

r2 - r1 = 9 i - 12 j - (1 i - 6 j)

r2 - r1 = 9 i - 12 j - 1 i + 6 j

r2 - r1 = 8 i - 6 j

The object´s displacement vector is Δr =  8i - 6 j  

firearm identification is the process of analyzing the bullets and cartridge cases left at a crime scene to determine if they came from a particular firearm. marks on the bullets and cartridges may be common to every firearm of that type. these are called class characteristics.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west