Question

Circular motion and projectile motion. The final answer I am asking for is the acceleration in metres per second squared. You will have to calculate the speed first, but the only answer you enter is the acceleration.

A young child whirls a stone in horizontal circle of radius 2.34 metres at a height of 1.17 metres above the ground. The string breaks and the stone flies off horizontally. It behaves like a projectile and strikes the ground after travelling a horizontal distance of 9.1 metres. What is the magnitude of the centripetal acceleration during the circular motion? You will have to calculate the speed first, but the only thing I am asking for is the magnitude. Remember to give me the number only as this silly program cannot handle scientific notation or units.

Hint" Projectile means that while it is moving through the air the only acceleration is that due to gravity. Assume a magnitude of 9.81 m/s².

Answer 1

Equations for projectile motion:
vt = l
h = 1/2 gt^2
where ? = 9.1 ?, ℎ = 1.17 ?

Therefore, initial speed of stone equals:
? =l/√(2 ∗ℎ/?)
And centripetal acceleration:
? = v^2/r
a = l^2g/2rh = 9.1*9.1*9.81/(2*2.34*1.17)
= 148.36 ?/?2
Answer: 148.36