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1. The ocean's level is currently rising at about 1.5 mm per year. At this rate, in how many years will sea level be 3 meters higher than now? 2. What is the acceleration of a vehicle that changes its velocity from 100 km/h to a dead stop in 10 s? 3. A racing car moving at 10 m/s north increases its velocity to 16 m/s north in a time interval of 3 s. What is its average acceleration during this time interval? What is the direction of this acceleration? 4. A ball is thrown straight up with an initial speed of 30 m/s, How high does it go, and how long is it in the air (neglecting air resistance)?

Question

  1. The ocean's level is currently rising at about 1.5 mm per year. At this rate, in how many years will sea level be 3 meters higher than now?
  2. What is the acceleration of a vehicle that changes its velocity from 100 km/h to a dead stop in 10 s?
  3. A racing car moving at 10 m/s north increases its velocity to 16 m/s north in a time interval of 3 s. What is its average acceleration during this time interval? What is the direction of this acceleration?
  4. A ball is thrown straight up with an initial speed of 30 m/s, How high does it go, and how long is it in the air (neglecting air resistance)?
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Solution

  1. To convert meters to millimeters, we know that 1 meter is equal to 1000 millimeters. So, 3 meters is equal to 3000 millimeters. If the sea level is rising at 1.5 mm per year, we can find out how many years it will take for the sea level to rise 3 meters by dividing 3000 mm by 1.5 mm/year. This gives us 2000 years.

  2. First, we need to convert the velocity from km/h to m/s because the standard unit of velocity in physics is m/s. We know that 1 km/h is approximately equal to 0.278 m/s. So, 100 km/h is equal to 100 * 0.278 = 27.8 m/s. Acceleration is the change in velocity divided by the time it takes for the change to occur. In this case, the change in velocity is 27.8 m/s (since the vehicle comes to a stop, the final velocity is 0 m/s). The time it takes for this change is 10 s. So, the acceleration of the vehicle is (0 m/s - 27.8 m/s) / 10 s = -2.78 m/s². The negative sign indicates that this is a deceleration, or a slowing down.

  3. Acceleration is the change in velocity divided by the time it takes for the change to occur. In this case, the change in velocity is 16 m/s - 10 m/s = 6 m/s. The time it takes for this change is 3 s. So, the average acceleration of the racing car is 6 m/s / 3 s = 2 m/s². The direction of this acceleration is the same as the direction of the velocity, which is north.

  4. The maximum height reached by the ball can be calculated using the equation h = v² / (2g), where v is the initial speed and g is the acceleration due to gravity (approximately 9.8 m/s²). Substituting the given values, we get h = (30 m/s)² / (2 * 9.8 m/s²) = 45.9 m. The total time the ball is in the air can be calculated using the equation t = 2v / g. Substituting the given values, we get t = 2 * 30 m/s / 9.8 m/s² = 6.12 s.

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