Technically, the question should state that the coin is tossed UPWARD from the top of the cliff.

h = at^2 + bt + C
find h for t = 5

rephrase: h = 25a + 5b + c

(1) 24 = 0.25a + 0.5b + c This is a different equation from the rephrased equation above, since the coeffient for c is 1 in both equations, but the coefficients for b are 5 and 0.5 respectively. Since there are 3 variables and only two different questions, we can't solve.

(2) 1.5 = 0.04a + 0.008b + 0.0016c This is the SAME equation as the rephrased equation above. The coefficients for c are 1 and 0.0016 respectively. .0016/.0016 = 1. Divide the other coefficients in this equation by .0016 also to see what happens.
.008/.0016 = 5
.04/.0016 = 25
So if I divide the entire equation given by statement 2 by .0016, I get:
937.5 = 25a + 5b + c. When I compare with my rephrased equation, I see that h must be 937.5.