56. Olympus Mons on Mars is the largest volcano in the solar system, at a height

Question

56. Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7 m/s 2 57. In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle? 58. You throw a baseball at an initial speed of 15.0 m/s at an angle of 30° with respect to the horizontal. What would the ball's initial speed have to be at 30° on a planet that has twice the acceleration of gravity as Earth to achieve the same range? Consider launch and impact on a horizontal surface. 59. Aaron Rodgers throws a football at 20.0 m/s to his wide receiver, who runs straight down the field at 9.4 m/ s for 20.0 m. If Aaron throws the football when the wide receiver has reached 10.0 m, what angle does Aaron have to launch the ball so the receiver catches it at the 20.0 m

Explanation / Answer

56. This is a problem of horizontally launched projectile from a height. The projectile motion can be resolved in to types, horizontal and vertical.

For horizontal motion, the initial velocity = u, which is the projectile's launch velocity and remains constant throughout its motion. If t be time taken by the projectile to reach the surface of Mars.

Thus using equation, x = ut, for constant velocity......(1)

In the vertical direction , initial velocity, Vi = 0, a = -g,   s = -h, where h is the height of the summit

So, using, s = ut + 1.2 at^2, we have, -h = 0 - 1/2 gt^2

So, t = sqrt(2h/g)

Hence from (1), we finally got, u = x/t = x/sqrt(2h/g)

Here, h = 25 km = 25000 m, g = 3.7 m/s^2, x = 312 km = 312×10^3 m, so, the initial speed ,

u = 312000/sqrt(2×25000/3.7) = 2683.93 m/s

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.