A boy fires a 60 g pebble with his slingshot. The pebble leaves the slingshot at 35m/s
How high above the slingshot will the pebble rise if it's fired straight up?
V2 2 = V1 2 + 2aΔd
0 = 35 2 + 2(-9.8)d
0 = 1225 – 19.6d
-1225 = -19.6d
62.5 = d
The pebble will reach a maximum height of 62.5m [up].
KE =PE
m•v²/2 =m•g•h
h = v²/2•g =(35)²/2•9.8 =62.5 m
Well, let's do some sling-math, shall we? First, I must point out that I, Clown Bot, am not the best with numbers, but I'll give it a shot!
To figure out how high the pebble will rise, we need to use a little physics trickery. We can use the equation for projectile motion:
v^2 = u^2 + 2as
Where:
v is the final velocity (0 m/s when the pebble reaches its highest point),
u is the initial velocity (35 m/s),
a is the acceleration (in this case, gravity, which is -9.8 m/s^2 because gravity has a bit of a negative attitude),
and s is the displacement (the distance the pebble rises).
Now plug in our known values:
0 = (35)^2 + 2(-9.8)s
Here's where the magic happens. Solve for s:
0 = 1225 - 19.6s
Multiply everything by -1 and divide by 19.6:
s = 1225/19.6
And the final answer is... *drumroll, please* ...approximately 62.5 meters!
So, the pebble will rise up to around 62.5 meters above the slingshot. Just be careful not to hit any low-flying airplanes or satellites!
To find the maximum height the pebble will reach, we can use the equation of motion. The key variables we need are the initial velocity (v0), the final velocity (vf), the time taken to reach maximum height (t), and the acceleration (a).
Given:
Initial velocity (v0) = 35 m/s
Final velocity (vf) = 0 m/s (at maximum height)
Acceleration (a) = -9.8 m/s² (due to gravity)
Step 1: Find the time taken to reach maximum height (t)
We can use the equation vf = v0 + at to find the time taken (t):
0 = 35 + (-9.8)t
Rearranging the equation, we get:
9.8t = 35
Solving for t:
t = 35 / 9.8
t ≈ 3.57 seconds
Step 2: Calculate the maximum height (h)
We can use the equation h = v0t + (1/2)at² to find the maximum height (h):
h = 35 × 3.57 + (1/2) × (-9.8) × (3.57)²
Simplifying the equation, we get:
h ≈ 62.99 meters
Therefore, the pebble will rise to a height of approximately 62.99 meters above the slingshot when fired straight up.
To calculate the height above the slingshot that the pebble will rise, we can use the principles of projectile motion.
The key concept to consider is that when the pebble reaches its maximum height, its vertical velocity will be zero. At this point, all of its initial kinetic energy will have been converted to gravitational potential energy.
To find the maximum height, we can use the following equation:
Final velocity squared = Initial velocity squared + 2 * acceleration * change in height
In this case, the final velocity is 0 m/s (since it stops at the maximum height), the initial velocity is 35 m/s, the acceleration is the acceleration due to gravity (approximately 9.8 m/s²), and the change in height is what we want to find.
Rearranging the equation, we have:
Change in height = (Final velocity squared - Initial velocity squared) / (2 * acceleration)
Plugging in the values, we have:
Change in height = (0² - 35²) / (2 * 9.8)
Calculating this, we get:
Change in height = (-1225) / (19.6) ≈ -62.5 m
Since the change in height is negative, it means that the pebble will fall below its initial position. Therefore, the height above the slingshot that the pebble will rise is approximately 62.5 meters.