Question

A marble was thrown vertically up the air and came back down to the samelevel in 1.6 s. (using g = 9.81 ms?).(a) What is it initial velocity?(b) What would be the highest height it can reach?(c) How long would it take to reach the highest point?

Answer 1

(a) 15.7 m/s

(b) 12.56 m

(c) 0.8 sec

Explanation:

We can calculate the initial velocity using the following formula:

(a)

`\begin{gathered} v=u+a\cdot t \\ v=0 \\ \text{therefore:} \\ u=-a\cdot t \\ \text{ replacing} \\ u=-(-9.81\cdot1.6) \\ u=15.7\text{ m/s} \end{gathered}`

(b)

We calculate the height in this way:

`\begin{gathered} h=((-u)^2)/(2g) \\ \text{ replacing} \\ h=((-15.7)^2)/(2\cdot9.81) \\ h=12.56\text{ m} \end{gathered}`

(c)The time to reach this height would be half the time it takes for the entire journey, that is, 0.8 seconds