# A projectile thrown from the ground level at an angle of alpha, is vertically displaced 35 meters within the last one second before landing.How many meters might it have raised ? (Assume ;g=10 N/kg,There is no drag)

Apr 25, 2016

$80 m$

#### Explanation:

As understood the problem.

Let $h$ be the height from which the projectile starts its downward flight. Also let $t$ be the time of downward flight. Let this point be origin.
As drag is to be ignored,
Kinematic equation is
$s = u t + \frac{1}{2} g {t}^{2}$, inserting given values
${h}_{t} = \frac{1}{2} \times 10 {t}^{2} = 5 {t}^{2}$ .....(1)

Let us find distance of flight in time $t - 1$
${h}_{t - 1} = 5 {\left(t - 1\right)}^{2}$ .....(2)

It is given that displacement in ${t}^{t h}$ second is 35 meters. Subtracting (2) from (1) and setting it equal to the given value.
${h}_{t} - {h}_{t - 1} = 5 {t}^{2} - 5 {\left(t - 1\right)}^{2} = 35$, Simplifying and solving for $t$

$5 {t}^{2} - 5 \left({t}^{2} - 2 t + 1\right) = 35$
or $\left(10 t - 5\right) = 35$
$\implies t = 4 s$

From (1)
${h}_{t} = 5 \times {4}^{2}$
$= 80 m$