4.You’re driving a car that can climb a maximum gradient of 500m/km. The hill in front of you starts at an elevation of 20m and reaches 100m. The total distance up the hill is 1.5km? What is the gradient of the hill and will your car make it?

Gradient of the hill is 53.33m/km which is lesser than the 500 m/km. So, he will be able to climb the hill conveniently.

Explanation: Given that

Maximum gradient = 500 m/km

Total distance = 1.5 km

Starting elevation = 20 m

Final elevation = 100 m

Gradient = change in elevation/ total distance.

Now, substitute the values into the formula.

Gradient = (100m - 20m)/1.5km

= 80m/1.5km

= 53.33m/km

Gradient of the hill is 53.33m/km which is lesser than the 500 m/km. So, he will be able to climb the hill conveniently.

the average speed is 24.57 km/hr

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft