Video Transcript
A particle is projected vertically
upward at seven meters per second from a point 38.7 meters above the ground. Find the maximum height the
particle can reach from the ground. Consider the acceleration due to
gravity to be 9.8 meters per second squared.
Let’s begin by sketching a diagram
modeling the situation. We are told that a particle is
projected vertically upwards at seven meters per second. We will call this initial velocity
𝑢. The point at which the particle is
projected from is 38.7 meters above the ground. And we are asked to find the
maximum height the particle can reach from the ground. We know that at this maximum
height, the velocity of the particle will be equal to zero. Finally, we are told that the
acceleration due to gravity is equal to 9.8 meters per second squared, and we know
that this will act vertically downwards.
In order to find the height ℎ, we
will begin by finding the displacement of the particle from its initial position to
its maximum height. We will call this displacement 𝑠
meters.
We can do this using the equations
of motion or SUVAT equations. If we let the positive direction be
vertically upwards, we have 𝑢 is equal to seven meters per second and 𝑣 is equal
to zero meters per second. Since gravity is acting in the
negative direction, 𝑎 is equal to negative 9.8 meters per second squared. We are trying to calculate the
displacement 𝑠. We will use the equation 𝑣 squared
is equal to 𝑢 squared plus two 𝑎𝑠.
Substituting in our values, we have
zero squared is equal to seven squared plus two multiplied by negative 9.8
multiplied by 𝑠. This simplifies to zero is equal to
49 minus 19.6𝑠. We can then add 19.6𝑠 to both
sides. And dividing through by 19.6, 𝑠 is
equal to 2.5. The displacement of the particle to
reach its maximum height is 2.5 meters. And we can therefore conclude that
the particle travels 2.5 meters vertically upwards.
The height above the ground at this
point will therefore be equal to 38.7 meters plus 2.5 meters. 38.7 plus 2.5 is equal to 41.2. And we can therefore conclude that
the maximum height the particle can reach from the ground is 41.2 meters.
