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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?

回答No.1

spring135 · ベストアンサー

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)