With what velocity must a body be projected vertically upward from the earth's surface,in the absence of friction,to rise to a height equal to the earth's radius (6400 km)? A)4.3 $\times$ 10⁵ m/s B)2.6 $\times$ 10³ m/s C)10⁵ m/s D)3.6 $\times$ 10² m/s E)7.9 $\times$ 10³ m/s

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Quizplus · Accepted Answer

To find the initial velocity required to project a body to a height equal to Earth's radius, we can use the formula derived from conservation of energy, specifically gravitational potential energy and kinetic energy. The formula is $v = \sqrt{2gR}$, where $v$ is the initial velocity, $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $R$ is the radius of the Earth (approximately $6.4 \times 10^6$ m). Plugging in the values, we get $v = \sqrt{2 \times 9.8 \times 6.4 \times 10^6} \approx 7.9 \times 10^3$ m/s, which matches choice E.

With What Velocity Must a Body Be Projected Vertically Upward ×\times×

With What Velocity Must a Body Be Projected Vertically Upward $\times$