physics intagral problem?

Question

After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by the following equation.

vector v=1.9i m/s-9.8tj m/s^2


The ball's displacement away from the edge of the table, during the time interval of 0.390 s during which it is in flight, is given by the following integral.

change of vector r = integral from 0 to .390 S of vector vdt

To perform the integral, you can use the calculus theorem below.

integral of A + Bf(x) dx = integral Adx + B integral of f(x) dx

You can think of the units and unit vectors as constants, represented by A and B. Do the integration to calculate the displacement of the ball.

find i hat

and find j hat

I know this looks confusing but I really need help with this problem.. thankyou

Answer 1

Basically the vector has a horizontal component, i, which has a constant velocity of 1.9 m/s; and a vertical component, j, which has an accelerating velocity -9.8*t

the integral of the vector is displacement
d(t, i, j)=1.9*t i-.5*9.8*t^2 j

To find the displacement in .39 seconds, plug that into the vector equation and crunch. Look at
d(t=0,i,j) versus d(t=0.39,i,j)

d(t=0,i,j)=(0i,0j)

d(t=0.39,i,j)=1.9*0.390i,
-.5*9.8*0.390^2j

=0.741i, -0.745j


j