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Chapter 3: Problem 60

Derive a general formula for the horizontal distance covered by a projectile launched horizontally at speed \(v_{0}\) from height \(h\)

Short Answer

Expert verified
The horizontal distance \(d\) of the projectile will be \(d = v_{0}\sqrt{\frac{2h}{g}}\).

Step by step solution

01

- Computing the Time of Flight

First, find the time it takes for the projectile to hit the ground, using the equation of motion in the vertical direction. This time, \(t\), can be calculated with the formula \( t =\sqrt{\frac{2h}{g}} \), where \(g\) is the acceleration due to gravity, typically \(9.8 m/s^2\) on Earth.
02

- Find the Horizontal Distance Covered

Second, once the time of flight is obtained, the horizontal distance d covered by the projectile can be determined using its initial horizontal speed \(v_{0}\) and the time of flight, \(t\). This can be calculated using the formula \(d = v_{0}t\).

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Most popular questions from this chapter

The position of an object as a function of time is \(\vec{r}=(3.2 t+\) \(\left.1.8 t^{2}\right) \hat{\imath}+\left(1.7 t-2.4 t^{2}\right) \hat{\jmath} \mathrm{m},\) with \(t\) in seconds. Find the object's acceleration vector.

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