A particle is initially 25 m above the ground and its height is h(t)=25+20t−5t² metres. Find the positive time, in seconds, when it reaches the ground.
Physics · Mathematical tools and vector · Quadratic Equation
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Question

A particle is initially 25 m above the ground and its height is h(t)=25+20t−5t² metres. Find the positive time, in seconds, when it reaches the ground.

G1 Physics · Accepted Answer

Set h=0: 25+20t−5t²=0. Divide by −5: t²−4t−5=0=(t−5)(t+1). The roots are 5 and −1. Negative time is outside the physical domain, so the particle reaches the ground at 5 s.