ACT Science Practice Test 45

Engineers studied the trajectories of a cannonball launched from a cannon under various conditions.

Study 1

On a level surface during a mild day, engineers launched a cannonball from a cannon as shown in Figure 1.

Figure 1

A camera was fixed atop the cannon so that it would point in the direction of the cannonball's launch. A receiver was also fixed to the cannon to record the cannonball's position as recorded by the camera.

As the cannonball traveled through the air, angle θ, which is defined in Figure 1, consistently changed. The change in θ was captured by the camera every 0.25 seconds after launch until the cannonball landed. For each recorded image, θ was measured (Figure 2).

Figure 2

Furthermore, every 0.25 sec after launch, the receiver sent out a radar pulse, part of which was reflected by the cannonball to the receiver. The roundtrip travel time of each pulse was recorded to determine the distance, d, between the receiver and the ball at any given time (see Figure 3).

Figure 3

Using d and θ, the engineers determined the ball's height, h, and distance, r, at the end of each 0.25 sec interval. A curve plotting h versus r was constructed.

This procedure was followed using cannonball launch starting speeds of 135 ft/sec, 150 ft/sec, and 180 ft/sec. For each launch speed, the ball was launched at θ = 30°. The curves representing h and r for each of the launch speeds were connected by lines for time, t = 2 sec, 3 sec, 4 sec, and 5 sec after launch (see Figure 4).

Figure 4

Study 2

Using an algorithm, the engineers calculated h and r at 0.25 sec intervals for the same cannonball launched in a vacuum in otherwise similar conditions to those in Study 1. The results are plotted in Figure 5.

Figure 5

The apoptotic index (AI) for a group of dividing cells is calculated as follows:

Figure 1 shows the AI for a culture of fibroblast cells as a function of the surrounding concentration in parts per million (ppm) of a cell toxin.

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Figure 1

One thousand actively dividing fibroblast cells in culture were studied. Figure 2 shows the distribution of the cells in each of the stages of the dividing cell cycle.

Figure 2

Electron micrographs were taken of the fibroblasts in culture. Figure 3 shows an example of cells in each of the 4 stages of the dividing cell cycle. Although the cells are not arranged in the sequence of the cell cycle, each stage is shown only once.

Figure 3

A polymorphism is the persistent occurrence of different appearances for a particular trait in a species. All humans have slight differences in their genotypes (genetic code) that result in different phenotypes (observable characteristics). Genetic polymorphisms are persistent variations in gene sequences at a particular location in chromosomes, such as those accounting for different blood types. Variations that cannot be observed with the naked eye require techniques such as capillary electrophoresis (the separation of genetic or protein material based on charge characteristics using an electric field).

The label on a vial of blood from a hospital patient was lost. The sample just tested positive for a disease of the blood protein hemoglobin that is very common in the hospital population. The sample was traced to a room with 4 patients who were subsequently tested to determine the source of the initial vial.

Tests and Results

Smears of the blood from the unidentified patient (P) and from the 4 newly tested patients (1–4) were observed under the microscope for the appearance of the blood cells. Results are shown in Table 1.

Table 1

Patient Blood smear findings

P Sickle cells

1 Target cells

2 Sickle cells

3 Normal blood cells

4 Sickle cells

Serum was isolated from the blood of Patient P and from Patients 1–4 and placed in separate tubes. A buffer was added to each vial to establish a pH of 8.6. One at a time, samples from each tube were injected into the capillary electrophoresis device set at 7.5 kilovolts (kV) to separate the types of hemoglobin present into peaks. The hemoglobin proteins composing a peak had similar charge characteristics. Figure 1 shows the peaks that resulted from all 5 samples.

Figure 1

To help design a carnival game, bowling balls at rest on the ground are launched along a track by a constant force spring apparatus as shown in Figure 1.

Figure 1

To win the game, the ball must pass Point Y but not Point Z. A total of 5 trials were done to determine the best design. For each combination of ball friction coefficient, μ, and ramp angle, θ, Point W was put at a distance, d, from Point X such that the ball will just barely reach Point Z before rolling back toward the ramp.

The ball's kinetic energy (KE) at Points X and Y along with its potential energy (PE) at Point Y are shown in joules (J) in Table 1 for each trial. The mechanical energy (ME) of the ball at any given point is the sum of its kinetic and potential energies. It should remain constant provided no energy is lost in the form of heat from friction or drag forces.