# What height will a dart achieve 7 seconds after being blown straight up at 50 m/s?

Oct 12, 2014

It is 100 m

Since this is motion in only one dimension, it is a relatively simple problem to solve.

As we're given time, acceleration and initial velocity, we can use our time dependent equation of kinematics, which is:

$\Delta y = {v}_{o} t + \frac{1}{2} a {t}^{2}$

Now let's list out our given values:

$t = 7$ seconds
${v}_{o} = 50$m/s
$a = - 9.8$m/${s}^{2}$ (Gravity acting downwards)

So now all we need to do is plug in and solve:

$\Delta y$ = 50(7) + $\frac{1}{2}$(-9.8)(${7}^{2}$)

$\Delta y =$109.9 m#

However, we would round this down to 100 because of the 1 significant digit in our given information (if you have 50. and 7.0, you would round it to 2 sig figs, which would be 110).

Hope that helped :)