## Related questions with answers

Two cannonballs, A and B, are fired from the ground with identical initial speeds, but with $\theta_{\mathrm{A}}$ larger than $\theta_{\mathrm{B}}$. Which travels farther?

Solutions

VerifiedThe maximum range happens for an object launched at $45^{\circ}$. If $\theta_A$ is less than $45^{\circ}$ then cannonball A travels further than cannonball B.

However if $\theta_A$ is greater than $45^{\circ}$ then cannonball B travels further than cannonball A.

Time for gravity to slow the projectile to zero vertical velocity $=\frac{V_y}{g} \\$ Time projectile is in the air$=$$\frac{2V_y}{g}$

The higher the angle the longer the projectile will spend in the air. The lower the angle the faster the projectile will travel horizontally while its in the air. The maximum distance traveled is when the angle is 45 degrees. So the cannonball with the angle closest to 45$\text{\textdegree}$ will travel farthest.

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