A baseball diamond is a square with side 90 ft. a batter hits the ball and runs toward first base with a speed of 24 ft/s.

Question

(a) At what rate is his distance from second base decreasing when he is halfway to first base?

(b) At what rate is his distance from third base increasing at the same moment?

Answer 1

draw a triangle vertexs:runner, secondbase, firstbase
a) x= distance to second base frm runner
90 ft = distance second to first
l= distance frm runner to first base

so l^2+90^2=x^2
and given dl/dt=24ft/sec

2l dl/dt+0=2xdx/dt
solve for dx/dt when l=45
you will have to calculalte x.

b. draw the traingle from second to runner to third to second. Set it up the same, same methodology