Name: __ 1. A 1260 g apple is dropped from the top of a 2700m high tower. If there is a frictional force of 4 Nacting up on it, determine how long it will take to reach a speed of 20m/s

Name: ______<br /><br />1. **Understanding the Problem:** An apple is falling from a great height, experiencing both gravity and air resistance (friction). We need to find the time it takes to reach a specific speed.<br /><br />2. **Known Values:**<br /><br />* Mass (m) = 1260 g = 1.26 kg<br />* Initial velocity (v₀) = 0 m/s (since it's dropped)<br />* Final velocity (v) = 20 m/s<br />* Height of tower = 2700 m (This information is extraneous for this particular problem since we are only concerned with the time it takes to reach 20 m/s, not the ground.)<br />* Frictional force (F_f) = 4 N<br />* Acceleration due to gravity (g) = 9.8 m/s²<br /><br />3. **Finding the Net Force:**<br /><br />The apple experiences two forces: gravity pulling it down and friction acting upwards. The net force (F_net) is the difference between these two:<br /><br />F_net = Force due to gravity - Frictional force<br />F_net = (m * g) - F_f<br />F_net = (1.26 kg * 9.8 m/s²) - 4 N<br />F_net = 12.348 N - 4 N<br />F_net = 8.348 N<br /><br />4. **Calculating the Acceleration:**<br /><br />Newton's second law of motion states F_net = m * a, where 'a' is the acceleration. We can rearrange this to solve for 'a':<br /><br />a = F_net / m<br />a = 8.348 N / 1.26 kg<br />a ≈ 6.625 m/s²<br /><br />5. **Finding the Time:**<br /><br />We can use the following equation of motion to find the time (t) it takes to reach the final velocity:<br /><br />v = v₀ + a*t<br /><br />Since the initial velocity is 0, the equation simplifies to:<br /><br />v = a*t<br /><br />Rearranging to solve for time:<br /><br />t = v / a<br />t = 20 m/s / 6.625 m/s²<br />t ≈ 3.02 s<br /><br />**Answer:** It will take approximately 3.02 seconds for the apple to reach a speed of 20 m/s.<br />