Answer
The car's speed at the gas station will be 1.4 m/s.
Work Step by Step
We can use conservation of energy to find the speed $v_2$ at the gas station. Therefore;
$KE_2+PE_2 = KE_1+PE_1$
$\frac{1}{2}mv_2^2+mg~h_2=\frac{1}{2}mv_1^2+mg~h_1$
$v_2^2=v_1^2+2g~(h_1-h_2)$
$v_2= \sqrt{v_1^2+2g~(h_1-h_2)}$
$v_2= \sqrt{(10~m/s)^2+(2)(9.80~m/s^2)(10~m-15~m)}$
$v_2 = 1.4~m/s$
The car's speed at the gas station will be 1.4 m/s.
