Question

Due to gravity is only 1.67 m/s. How fast was it going after 1.5 seconds?

Write a word problem using the information from the given equation and inequality. Be sure to include all seven parts and an appropriate question requesting a solution for the unknown (variable). The seven parts of a one-variable equation are as follows:
correct variable term for the left-side expression
correct constant term for the left-side expression
correct operation between the terms of the left-side expression
correct equal sign or inequality symbol
correct variable term for the right-side expression
correct constant term for the right-side expression
correct operation between the terms of the right-side expression.

Answer 1

The final velocity of a rock thrown downwards with an initial velocity of -13.0 m/s and falling an additional 5.10 meters under gravity is -16.4 m/s.

Step-by-step explanation:

The question involves kinematics, specifically calculating the final velocity of an object in free fall under the influence of gravity. According to the given information, if the body had an initial speed of -13.0 m/s and it is subject to an acceleration due to gravity -9.8 m/s², we use the kinematic equation v² = vo² + 2a(y - yo) to calculate the final velocity after falling -5.10 meters.

Plugging the given values into the equation, we get v² = (-13.0 m/s)² + 2(-9.80 m/s²)(-5.10 m - 0 m) = 268.96 m²/s². Taking the square root, we find v = ±16.4 m/s. Given the direction of gravity and the initial velocity, the negative root applies, therefore the final velocity is v = -16.4 m/s.

To construct a word problem using this information, we can state:
'A rock is thrown downwards from a cliff with an initial speed of 13.0 m/s. As it falls under gravity, with no other forces acting upon it such as air resistance, how fast is the rock going after it falls an additional 5.10 meters?'

Answer 2

The velocity of the object after 1.5 seconds due to gravity is approximately -5.70 m/s.

Step-by-step explanation:

The question asks how fast an object is going after 1.5 seconds due to gravity.

To find the final velocity, we can use the kinematic equation v² = vo² + 2a(y - yo), where v is the final velocity, vo is the initial velocity, a is the acceleration, y is the final position, and yo is the initial position. Given that yo = 0, y = -1.67 m, vo = 0 m/s, and a = -9.8 m/s² (assuming downward as negative), we can substitute these values into the equation:

v² = (0 m/s)² + 2(-9.8 m/s²)(-1.67 m)
= 32.4 m²/s²

After taking the square root of 32.4, we get v ≈ ±5.70 m/s. We choose the negative root to indicate that the object is still moving downward. Therefore, the velocity of the object after 1.5 seconds is approximately -5.70 m/s.