この問題の解き方と答えをおしえてください

この問題の解き方と答えをおしえてください。

問題文が英語になってしまいますがよろしくおねがいします。

The height h, in meters, at some time t, in seconds, of an object propelled upward at a speed of 82 meters per second from an initial height of 103 meters is given by the function h(t)=-10t^2+82t+103.

a) What is the maximum height of the object?

b) When will the object be above 200 meters high?

c) When will the object hit the ground?

No.1 ベストアンサー 回答者： spring135 回答日時： 2009/12/17 16:36

a) h(t)=-10(t^2-8.2t)+103=-10(t-4.1)^2+103+168.1

==-10(t-4.1)^2+271.1
the maximum height is 271.1(meter)
b) h(t)=-10t^2+82t+103=200
10t^2-82t+97=0
t=(82±(82^2-4*10*97)^0.5)/2/10=1.435, 6.765
1.43<t<6.77(sec)
c)h(t)=-10t^2+82t+103=0
t>0, t=9.31(sec)