Mathematics: Two competing catapults launch pumpkins. Catapult A launches from a starting height of 10ft and an initial upward velocity of 45ft/sec. Catapult B launches from a starting height of 25ft and an initial upward velocity of 40ft/sec. Which pumpkin, A or B, achieves a greater maximum height?

If she used rounding she would’ve gotten -25×10 equals -250...

Two competing catapults launch pumpkins. Catapult

Ответ:

dmgcity

20.01.2022

Mathematics

For these projectiles,

${v_f}^2-{v_i}^2=-2g(y_{\rm max}-y_i)$

where v_f is the projectile's final velocity (which is 0 at maximum height), v_i is its initial velocity, $g=9.80\frac{\rm m}{\mathrm s^2}$ is the acceleration due to gravity, and y_i is its initial height.

Let y_A,y_B denote the maximum heights of pumpkins A and B, respectively. Then

$-\left(45\dfrac{\rm ft}{\rm s}\right)^2=-2g(y_A-10\,\mathrm{ft})\implies y_A=113\,\mathrm{ft}$

$-\left(40\dfrac{\rm ft}{\rm s}\right)^2=-2g(y_B-25\,\mathrm{ft})\implies y_B=107\,\mathrm{ft}$

So pumpkin A reaches a greater maximum height.

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Two competing catapults launch pumpkins. Catapult A launches from a starting height of 10ft and an initial upward velocity of 45ft/sec. Catapult B launches from a starting height of 25ft and an initial upward velocity of 40ft/sec. Which pumpkin, A or B, achieves a greater maximum height?

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