a. A truck loaded with cannonball watermelons stops suddenly to avoid running over the edge of a washed-out bridge (see figure 1). The quick stop causes a number of melons to fly off the truck. One melon rolls over the edge with an initial speed vi = 14.0 m/s in the horizontal direction. A cross-section of the bank has the shape of the bottom half of a parabola, with its vertex at the initial location of the projected watermelon and with the equation y2 = 12x, where x and y are measured in meters. What are the x and y coordinates of the melon when it splatters on the bank? b. From the relationship between the launch angle ?, and the horizontal range R, for a dart launched with a speed v. This assumed that the launcher and the target were on the same horizontal level. Relax this assumption and place the launcher at some elevation h above the target, as in figure 2. i. Derive the symbolic equation relating the range R, to the launch angle ?, launch speed v, launcher elevation h, and magnitude of gravitational acceleration g. ii. Check that when setting h to zero, you recover the result from the lab, and enter the equation below. iii. Assume the target (which was a wheel) had a diameter of 10 cm. If the distance to the target centre was R=1.1 m and your launch speed was v=5.3 ms−1, then what is the tolerance on setting the angle in degrees (use a positive value)? iv. Do you think you were able to set the launch angle to this precision with your design?
a. A truck loaded with cannonball watermelons stops suddenly to avoid running over the edge of a washed-out bridge (see figure 1). The quick stop causes a number of melons to fly off the truck. One melon rolls over the edge with an initial speed vi = 14.0 m/s in the horizontal direction. A cross-section of the bank has the shape of the bottom half of a parabola, with its vertex at the initial location of the projected watermelon and with the equation y2 = 12x, where x and y are measured in meters. What are the x and y coordinates of the melon when it splatters on the bank?
b. From the relationship between the launch angle ?, and the horizontal range R, for a dart launched with a speed v. This assumed that the launcher and the target were on the same horizontal level. Relax this assumption and place the launcher at some elevation h above the target, as in figure 2.
i. Derive the symbolic equation relating the range R, to the launch angle ?, launch speed v, launcher elevation h, and magnitude of gravitational acceleration g.
ii. Check that when setting h to zero, you recover the result from the lab, and enter the equation below.
iii. Assume the target (which was a wheel) had a diameter of 10 cm. If the distance to the target centre was R=1.1 m and your launch speed was v=5.3 ms−1, then what is the tolerance on setting the angle in degrees (use a positive value)?
iv. Do you think you were able to set the launch angle to this precision with your design?
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